{"id":4622,"date":"2026-08-30T09:42:40","date_gmt":"2026-08-30T09:42:40","guid":{"rendered":"https:\/\/cosmalore.com\/ar\/?p=4622"},"modified":"2026-08-30T09:42:40","modified_gmt":"2026-08-30T09:42:40","slug":"mathematical-algorithms","status":"publish","type":"post","link":"https:\/\/cosmalore.com\/ar\/2026\/08\/30\/mathematical-algorithms\/","title":{"rendered":"\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629"},"content":{"rendered":"<p>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0647\u064a \u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0645\u0646\u0637\u0642\u064a\u0629 \u0648\u0645\u0646\u0638\u0645\u0629 \u062a\u062a\u0643\u0648\u0646 \u0645\u0646 \u062e\u0637\u0648\u0627\u062a \u0645\u062d\u062f\u062f\u0629 \u0644\u062d\u0644 \u0645\u0633\u0623\u0644\u0629 \u0631\u064a\u0627\u0636\u064a\u0629\u060c \u0623\u0648 \u0644\u0625\u062c\u0631\u0627\u0621 \u0639\u0645\u0644\u064a\u0629 \u062d\u0633\u0627\u0628\u064a\u0629\u060c \u0623\u0648 \u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u062e\u0627\u0635\u064a\u0629\u060c \u0623\u0648 \u0644\u0628\u0646\u0627\u0621 \u0643\u0627\u0626\u0646 \u0631\u064a\u0627\u0636\u064a\u060c \u0623\u0648 \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062a\u0642\u0631\u064a\u0628 \u0639\u062f\u062f\u064a \u0644\u0646\u062a\u064a\u062c\u0629 \u064a\u0635\u0639\u0628 \u062d\u0633\u0627\u0628\u0647\u0627 \u0628\u0635\u0648\u0631\u0629 \u0645\u0628\u0627\u0634\u0631\u0629. \u0648\u0639\u0644\u0649 \u0627\u0644\u0631\u063a\u0645 \u0645\u0646 \u0627\u0631\u062a\u0628\u0627\u0637 \u0643\u0644\u0645\u0629 \u00ab\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629\u00bb \u0627\u0644\u064a\u0648\u0645 \u0628\u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0648\u0627\u0644\u0628\u0631\u0645\u062c\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0623\u0642\u062f\u0645 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0627\u0644\u062d\u062f\u064a\u062b\u061b \u0641\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631 \u062a\u0631\u062c\u0639 \u0641\u064a \u0623\u0635\u0644\u0647\u0627 \u0625\u0644\u0649 \u0643\u062a\u0627\u0628 \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0644\u0625\u0642\u0644\u064a\u062f\u0633 \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062b\u0627\u0644\u062b \u0642\u0628\u0644 \u0627\u0644\u0645\u064a\u0644\u0627\u062f\u060c \u0648\u0647\u064a \u0645\u062b\u0627\u0644 \u0645\u0628\u0643\u0631 \u0639\u0644\u0649 \u0625\u062c\u0631\u0627\u0621 \u0631\u064a\u0627\u0636\u064a \u0645\u062a\u0633\u0644\u0633\u0644 \u0648\u062f\u0642\u064a\u0642 \u0645\u0627 \u064a\u0632\u0627\u0644 \u0645\u0633\u062a\u062e\u062f\u0645\u0627\u064b \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Algorithm\" title=\"1|Algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[1]<\/a><\/sup><sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Euclidean_algorithm\" title=\"2|Euclidean algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[2]<\/a><\/sup><\/p>\n<div class=\"infobox\">\n<table>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0627\u0633\u0645<\/td>\n<td class=\"ib-val\">\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0628\u0627\u0644\u0625\u0646\u062c\u0644\u064a\u0632\u064a\u0629<\/td>\n<td class=\"ib-val\">Mathematical Algorithms<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0645\u0641\u0647\u0648\u0645<\/td>\n<td class=\"ib-val\">\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0645\u062d\u062f\u062f\u0629 \u0648\u0645\u0646\u0638\u0645\u0629 \u0644\u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0631\u064a\u0627\u0636\u064a\u0629 \u0623\u0648 \u062d\u0633\u0627\u0628\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0645\u062f\u062e\u0644\u0627\u062a\u060c \u062e\u0637\u0648\u0627\u062a\u060c \u0634\u0631\u0648\u0637\u060c \u062a\u0643\u0631\u0627\u0631\u060c \u0648\u0645\u062e\u0631\u062c\u0627\u062a<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0647\u062f\u0641<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 \u062f\u0642\u064a\u0642\u0629 \u0623\u0648 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0628\u0637\u0631\u064a\u0642\u0629 \u0645\u0646\u0647\u062c\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0645\u062c\u0627\u0644\u0627\u062a \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f<\/td>\n<td class=\"ib-val\">\u0627\u0644\u0642\u0648\u0627\u0633\u0645\u060c \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629\u060c \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u062c\u0628\u0631<\/td>\n<td class=\"ib-val\">\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0648\u062a\u062d\u0644\u064a\u0644 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a<\/td>\n<td class=\"ib-val\">\u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u062c\u0630\u0648\u0631 \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0648\u062d\u0644 \u0627\u0644\u0623\u0646\u0638\u0645\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a<\/td>\n<td class=\"ib-val\">\u062d\u0644 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0648\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0648\u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629<\/td>\n<td class=\"ib-val\">\u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629 \u0648\u0627\u0644\u062a\u0642\u0627\u0637\u0639\u0627\u062a \u0648\u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0648\u0627\u0644\u062a\u062d\u0648\u064a\u0644\u0627\u062a<\/td>\n<\/tr>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0623\u0645\u062b\u0644\u0629 \u062a\u0627\u0631\u064a\u062e\u064a\u0629 \u0648\u0645\u0634\u0647\u0648\u0631\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633<\/td>\n<td class=\"ib-val\">\u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u063a\u0631\u0628\u0627\u0644 \u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633<\/td>\n<td class=\"ib-val\">\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0636\u0645\u0646 \u062d\u062f \u0645\u0639\u064a\u0646<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0637\u0631\u064a\u0642\u0629 \u0646\u064a\u0648\u062a\u0646<\/td>\n<td class=\"ib-val\">\u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u064a \u0644\u062c\u0630\u0648\u0631 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u062d\u0630\u0641 \u0627\u0644\u063a\u0627\u0648\u0633\u064a<\/td>\n<td class=\"ib-val\">\u062d\u0644 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0633\u0631\u064a\u0639<\/td>\n<td class=\"ib-val\">\u062d\u0633\u0627\u0628 \u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0645\u062a\u0642\u0637\u0639 \u0628\u0643\u0641\u0627\u0621\u0629 \u0639\u0627\u0644\u064a\u0629<\/td>\n<\/tr>\n<tr class=\"ib-sec\">\n<td colspan=\"2\">\u0627\u0644\u062e\u0635\u0627\u0626\u0635<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0635\u062d\u0629<\/td>\n<td class=\"ib-val\">\u0625\u0646\u062a\u0627\u062c \u0646\u062a\u064a\u062c\u0629 \u062a\u062d\u0642\u0642 \u0627\u0644\u0645\u0637\u0644\u0648\u0628 \u0639\u0646\u062f \u0627\u0646\u0637\u0628\u0627\u0642 \u0627\u0644\u0634\u0631\u0648\u0637<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0627\u0646\u062a\u0647\u0627\u0621<\/td>\n<td class=\"ib-val\">\u062a\u0648\u0642\u0641 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0641\u064a \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u0635\u0645\u0645\u062a \u0644\u062d\u0644\u0647\u0627<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u0643\u0641\u0627\u0621\u0629<\/td>\n<td class=\"ib-val\">\u062a\u0642\u0627\u0633 \u0628\u0627\u0644\u0648\u0642\u062a \u0648\u0627\u0644\u0630\u0627\u0643\u0631\u0629 \u0648\u0639\u062f\u062f \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a<\/td>\n<\/tr>\n<tr class=\"ib-row\">\n<td class=\"ib-label\">\u0627\u0644\u062a\u0639\u0642\u064a\u062f<\/td>\n<td class=\"ib-val\">\u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0645\u0639 \u0646\u0645\u0648 \u062d\u062c\u0645 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a<\/td>\n<\/tr>\n<\/table>\n<div class=\"ib-foot\">COSMALORE \u00b7 \u0627\u0644\u0645\u0648\u0633\u0648\u0639\u0629 \u0627\u0644\u0639\u0631\u0628\u064a\u0629<\/div>\n<\/div>\n<h2>\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629<\/h2>\n<p>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0647\u064a \u0648\u0635\u0641 \u062f\u0642\u064a\u0642 \u0644\u0639\u0645\u0644\u064a\u0629 \u062d\u0633\u0627\u0628\u064a\u0629 \u0623\u0648 \u0627\u0633\u062a\u062f\u0644\u0627\u0644\u064a\u0629 \u062a\u0628\u062f\u0623 \u0628\u0645\u062f\u062e\u0644\u0627\u062a \u0645\u062d\u062f\u062f\u0629 \u0648\u062a\u0646\u0641\u0630 \u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u0627\u062a \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0645\u062e\u0631\u062c \u0645\u062d\u062f\u062f. \u0648\u062a\u0639\u0631\u0651\u0641\u0647\u0627 \u0627\u0644\u0645\u0631\u0627\u062c\u0639 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0628\u0648\u0635\u0641\u0647\u0627 \u062a\u0639\u0644\u064a\u0645\u0627\u062a \u062a\u0641\u0635\u064a\u0644\u064a\u0629 \u062a\u062d\u062f\u062f \u0639\u0645\u0644\u064a\u0629 \u062d\u0633\u0627\u0628\u064a\u0629 \u062a\u0628\u062f\u0623 \u0628\u0645\u062f\u062e\u0644 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0627\u0644\u0645\u0645\u0643\u0646\u0629\u060c \u0648\u062a\u0647\u062f\u0641 \u0625\u0644\u0649 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 \u0623\u0648 \u0645\u062e\u0631\u062c \u062a\u062d\u062f\u062f\u0647 \u062a\u0644\u0643 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Algorithm\" title=\"3|Algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[3]<\/a><\/sup><\/p>\n<p>\u0648\u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0623\u0628\u0633\u0637 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0628\u0631\u0627\u0645\u062c \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b\u0629. \u0641\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u0642\u0633\u0645\u0629 \u0627\u0644\u0645\u0637\u0648\u0644\u0629\u060c \u0648\u062e\u0637\u0648\u0627\u062a \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631\u060c \u0648\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062d\u0630\u0641 \u0644\u062d\u0644 \u0646\u0638\u0627\u0645 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0648\u062e\u0637\u0648\u0627\u062a \u062d\u0633\u0627\u0628 \u0627\u0644\u062c\u0630\u0631 \u0627\u0644\u062a\u0631\u0628\u064a\u0639\u064a \u0628\u0627\u0644\u062a\u0642\u0631\u064a\u0628\u060c \u0643\u0644\u0647\u0627 \u0623\u0645\u062b\u0644\u0629 \u0639\u0644\u0649 \u0639\u0645\u0644\u064a\u0627\u062a \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629. \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0644\u064a\u0633\u062a \u0645\u0631\u0627\u062f\u0641\u0629 \u0644\u0644\u0628\u0631\u0646\u0627\u0645\u062c\u061b \u0641\u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0647\u0648 \u062a\u0646\u0641\u064a\u0630 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0623\u0648 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0639\u0644\u0649 \u0622\u0644\u0629 \u0623\u0648 \u0646\u0638\u0627\u0645 \u062d\u0627\u0633\u0648\u0628\u064a\u060c \u0628\u064a\u0646\u0645\u0627 \u064a\u0645\u0643\u0646 \u0648\u0635\u0641 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0648\u062a\u0646\u0641\u064a\u0630\u0647\u0627 \u064a\u062f\u0648\u064a\u0627\u064b \u0645\u0646 \u062f\u0648\u0646 \u062d\u0627\u0633\u0648\u0628.<\/p>\n<h2>\u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0648\u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0648\u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a<\/h2>\n<p>\u064a\u062a\u0643\u0648\u0646 \u0627\u0644\u0628\u0646\u0627\u0621 \u0627\u0644\u0623\u0633\u0627\u0633\u064a \u0644\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0646 \u0645\u062f\u062e\u0644\u0627\u062a \u0648\u062e\u0637\u0648\u0627\u062a \u0648\u0645\u062e\u0631\u062c\u0627\u062a. \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0647\u064a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0628\u062f\u0623 \u0645\u0646\u0647\u0627 \u0627\u0644\u0639\u0645\u0644\u064a\u0629\u060c \u0648\u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0647\u064a \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0643\u064a\u0641\u064a\u0629 \u0645\u0639\u0627\u0644\u062c\u0629 \u0647\u0630\u0647 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a \u0647\u064a \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u062a\u064a \u062a\u0646\u062a\u062c \u0641\u064a \u0627\u0644\u0646\u0647\u0627\u064a\u0629. \u0648\u0642\u062f \u062a\u062d\u062a\u0648\u064a \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0639\u0644\u0649 \u0639\u0645\u0644\u064a\u0627\u062a \u062d\u0633\u0627\u0628\u064a\u0629\u060c \u0623\u0648 \u0645\u0642\u0627\u0631\u0646\u0627\u062a\u060c \u0623\u0648 \u0634\u0631\u0648\u0637\u060c \u0623\u0648 \u062a\u0643\u0631\u0627\u0631\u060c \u0623\u0648 \u0627\u0646\u062a\u0642\u0627\u0644 \u0628\u064a\u0646 \u0645\u0631\u0627\u062d\u0644 \u0645\u062e\u062a\u0644\u0641\u0629.<\/p>\n<p>\u0645\u062b\u0644\u0627\u064b\u060c \u064a\u0645\u0643\u0646 \u062a\u0635\u0645\u064a\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631 \u0644\u0639\u062f\u062f\u064a\u0646 \u0635\u062d\u064a\u062d\u064a\u0646. \u062a\u0628\u062f\u0623 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0628\u0627\u0644\u0639\u062f\u062f\u064a\u0646\u060c \u062b\u0645 \u062a\u062d\u0633\u0628 \u0628\u0627\u0642\u064a \u0642\u0633\u0645\u0629 \u0627\u0644\u0639\u062f\u062f \u0627\u0644\u0623\u0643\u0628\u0631 \u0639\u0644\u0649 \u0627\u0644\u0623\u0635\u063a\u0631\u060c \u0648\u062a\u0633\u062a\u0628\u062f\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u0646 \u0648\u0641\u0642 \u0642\u0627\u0639\u062f\u0629 \u0645\u062d\u062f\u062f\u0629\u060c \u0648\u062a\u0643\u0631\u0631 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u062d\u062a\u0649 \u064a\u0635\u0628\u062d \u0627\u0644\u0628\u0627\u0642\u064a \u0635\u0641\u0631\u0627\u064b. \u0622\u062e\u0631 \u0628\u0627\u0642 \u063a\u064a\u0631 \u0635\u0641\u0631\u064a \u0647\u0648 \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Euclidean_algorithm\" title=\"4|Euclidean algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[4]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0648\u0625\u062b\u0628\u0627\u062a \u0627\u0644\u0635\u062d\u0629<\/h2>\n<p>\u0644\u0627 \u064a\u0643\u0641\u064a \u0623\u0646 \u062a\u0628\u062f\u0648 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0639\u0642\u0648\u0644\u0629\u061b \u0628\u0644 \u064a\u062c\u0628 \u0625\u062b\u0628\u0627\u062a \u0623\u0646\u0647\u0627 \u062a\u0646\u062a\u062c \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0645\u0633\u062a\u0648\u0641\u064a\u0629 \u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0645\u0633\u0623\u0644\u0629. \u0648\u0644\u0630\u0644\u0643 \u062a\u0631\u062a\u0628\u0637 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0631\u062a\u0628\u0627\u0637\u0627\u064b \u0648\u062b\u064a\u0642\u0627\u064b \u0628\u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629.<\/p>\n<p>\u064a\u062a\u0636\u0645\u0646 \u0625\u062b\u0628\u0627\u062a \u0635\u062d\u0629 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u0627\u062f\u0629 \u0625\u062b\u0628\u0627\u062a \u0623\u0646 \u0643\u0644 \u062e\u0637\u0648\u0629 \u062a\u062d\u0627\u0641\u0638 \u0639\u0644\u0649 \u062e\u0627\u0635\u064a\u0629 \u0645\u0639\u064a\u0646\u0629 \u0623\u0648 \u062a\u0642\u0631\u0628\u0646\u0627 \u0645\u0646 \u0627\u0644\u0647\u062f\u0641\u060c \u062b\u0645 \u0625\u062b\u0628\u0627\u062a \u0623\u0646 \u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0634\u0631\u0637 \u0627\u0644\u062a\u0648\u0642\u0641 \u064a\u0639\u0646\u064a \u0623\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629 \u0642\u062f \u062a\u062d\u0642\u0642\u062a. \u0648\u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u064a\u0629 \u062a\u0633\u062a\u062e\u062f\u0645 \u0643\u062b\u064a\u0631\u0627\u064b \u0641\u0643\u0631\u0629 \u00ab\u0627\u0644\u062b\u0627\u0628\u062a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u00bb\u061b \u0648\u0647\u064a \u062e\u0627\u0635\u064a\u0629 \u062a\u0638\u0644 \u0635\u062d\u064a\u062d\u0629 \u0628\u0639\u062f \u0643\u0644 \u062f\u0648\u0631\u0629 \u0645\u0646 \u062f\u0648\u0631\u0627\u062a \u0627\u0644\u0639\u0645\u0644\u064a\u0629.<\/p>\n<h2>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633<\/h2>\n<p>\u062a\u0639\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u0645\u0646 \u0623\u0642\u062f\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u0648\u0623\u0643\u062b\u0631\u0647\u0627 \u062f\u0648\u0627\u0645\u0627\u064b. \u0648\u0635\u0641 \u0625\u0642\u0644\u064a\u062f\u0633 \u0641\u064a \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0637\u0631\u064a\u0642\u0629 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0642\u0633\u0645\u0629 \u0645\u0639 \u0627\u0644\u0628\u0627\u0642\u064a \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631. \u0648\u0625\u0630\u0627 \u0643\u0627\u0646 <i>a\u2265b&gt;0<\/i>\u060c \u0646\u0643\u062a\u0628:<\/p>\n<p><i>a=qb+r<\/i><\/p>\n<p>\u062d\u064a\u062b <i>0\u2264r&lt;b<\/i>\u060c \u062b\u0645 \u0646\u0633\u062a\u0628\u062f\u0644 \u0627\u0644\u0632\u0648\u062c <i>(a,b)<\/i> \u0628\u0627\u0644\u0632\u0648\u062c <i>(b,r)<\/i> \u0648\u0646\u0643\u0631\u0631 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u062d\u062a\u0649 \u064a\u0635\u0628\u062d \u0627\u0644\u0628\u0627\u0642\u064a \u0635\u0641\u0631\u0627\u064b. \u0622\u062e\u0631 \u0628\u0627\u0642 \u063a\u064a\u0631 \u0635\u0641\u0631\u064a \u0647\u0648 \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Euclidean_algorithm\" title=\"5|Euclidean algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[5]<\/a><\/sup><\/p>\n<p>\u0648\u0645\u0646 \u0623\u0647\u0645 \u062e\u0635\u0627\u0626\u0635 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0623\u0646\u0647\u0627 \u0644\u0627 \u062a\u062a\u0637\u0644\u0628 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u0646 \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644\u0647\u0645\u0627 \u0627\u0644\u0623\u0648\u0644\u064a\u0629. \u0643\u0645\u0627 \u0623\u0646 \u0639\u062f\u062f \u062e\u0637\u0648\u0627\u062a\u0647\u0627 \u064a\u0646\u0645\u0648 \u0628\u0628\u0637\u0621 \u0634\u062f\u064a\u062f \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u062d\u062c\u0645 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u061b \u0648\u062a\u0630\u0643\u0631 \u0627\u0644\u0645\u0631\u0627\u062c\u0639 \u0623\u0646 \u0639\u062f\u062f \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u064a\u0645\u0643\u0646 \u0631\u0628\u0637\u0647 \u0628\u0639\u062f\u062f \u062e\u0627\u0646\u0627\u062a \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a\u060c \u0648\u0647\u0648 \u0645\u0627 \u064a\u0641\u0633\u0631 \u0643\u0641\u0627\u0621\u062a\u0647\u0627 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0639\u062f\u062f\u064a \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Euclidean_algorithm\" title=\"6|Euclidean algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[6]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0627\u0644\u0645\u0648\u0633\u0639\u0629<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u062a\u0648\u0633\u064a\u0639 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u0628\u062d\u064a\u062b \u0644\u0627 \u062a\u0643\u062a\u0641\u064a \u0628\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631\u060c \u0628\u0644 \u062a\u062c\u062f \u0623\u064a\u0636\u0627\u064b \u0639\u062f\u062f\u064a\u0646 \u0635\u062d\u064a\u062d\u064a\u0646 <i>x<\/i> \u0648<i>y<\/i> \u064a\u062d\u0642\u0642\u0627\u0646:<\/p>\n<p><i>ax+by=gcd(a,b)<\/i><\/p>\n<p>\u0648\u0647\u0630\u0647 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0647\u064a \u0635\u064a\u063a\u0629 \u0645\u0646 \u0647\u0648\u064a\u0629 \u0628\u0632\u0648\u060c \u0648\u062a\u0624\u062f\u064a \u062f\u0648\u0631\u0627\u064b \u0645\u0647\u0645\u0627\u064b \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0648\u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629. \u0643\u0645\u0627 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0643\u0648\u0633 \u0627\u0644\u0636\u0631\u0628\u064a \u0644\u0639\u062f\u062f \u0641\u064a \u062d\u0633\u0627\u0628\u064a\u0627\u062a \u0645\u0639\u064a\u0627\u0631\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0639\u0643\u0648\u0633 \u0645\u0648\u062c\u0648\u062f\u0627\u064b.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629<\/h2>\n<p>\u062a\u062d\u062a\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0645\u0648\u0642\u0639\u0627\u064b \u0645\u0631\u0643\u0632\u064a\u0627\u064b \u0641\u064a \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629. \u0641\u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0627\u062e\u062a\u0628\u0627\u0631 \u0623\u0648\u0644\u064a\u0629 \u0639\u062f\u062f \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0637\u0631\u0642 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0643\u0645\u0627 \u062a\u0648\u062c\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0644\u062a\u0648\u0644\u064a\u062f \u0642\u0627\u0626\u0645\u0629 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u062d\u062a\u0649 \u062d\u062f \u0645\u0639\u064a\u0646\u060c \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0625\u0644\u0649 \u0639\u0648\u0627\u0645\u0644\u0647\u0627\u060c \u0648\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0648\u0627\u0644\u0642\u0648\u0627\u0633\u0645.<\/p>\n<p>\u0645\u0646 \u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629 \u063a\u0631\u0628\u0627\u0644 \u0625\u0631\u0627\u062a\u0648\u0633\u062a\u064a\u0646\u0633\u060c \u0627\u0644\u0630\u064a \u064a\u062a\u064a\u062d \u062a\u062d\u062f\u064a\u062f \u062c\u0645\u064a\u0639 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0627\u0644\u0623\u0635\u063a\u0631 \u0645\u0646 \u0623\u0648 \u0627\u0644\u0645\u0633\u0627\u0648\u064a\u0629 \u0644\u062d\u062f \u0645\u0639\u064a\u0646 \u0639\u0646 \u0637\u0631\u064a\u0642 \u0627\u0633\u062a\u0628\u0639\u0627\u062f \u0645\u0636\u0627\u0639\u0641\u0627\u062a \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0627\u0644\u0645\u0639\u0631\u0648\u0641\u0629 \u062a\u062f\u0631\u064a\u062c\u064a\u0627\u064b. \u0648\u0642\u062f \u0627\u0631\u062a\u0628\u0637\u062a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0623\u0648\u0644\u064a\u0629 \u0644\u0627\u062d\u0642\u0627\u064b \u0628\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0648\u0627\u0633\u0639\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0627\u0644\u062a\u0634\u0641\u064a\u0631.<\/p>\n<h2>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0628\u062d\u062b \u0639\u0646 \u0627\u0644\u062c\u0630\u0648\u0631<\/h2>\n<p>\u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0625\u064a\u062c\u0627\u062f \u062d\u0644 \u0644\u0644\u0645\u0639\u0627\u062f\u0644\u0629 <i>f(x)=0<\/i>. \u0648\u0641\u064a \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0644\u0627 \u064a\u0648\u062c\u062f \u062d\u0644 \u0645\u063a\u0644\u0642 \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647 \u0628\u0635\u064a\u063a\u0629 \u0628\u0633\u064a\u0637\u0629\u060c \u0648\u0644\u0630\u0644\u0643 \u062a\u0633\u062a\u062e\u062f\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0639\u062f\u062f\u064a\u0629 \u0644\u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645\u0629 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0644\u0644\u062c\u0630\u0631.<\/p>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 \u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u0646\u0635\u064a\u0641 \u0645\u062b\u0644\u0627\u064b \u0645\u062c\u0627\u0644\u0627\u064b \u064a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u062c\u0630\u0631\u060c \u062b\u0645 \u062a\u0642\u0633\u0645\u0647 \u0625\u0644\u0649 \u0646\u0635\u0641\u064a\u0646 \u0628\u0635\u0648\u0631\u0629 \u0645\u062a\u0643\u0631\u0631\u0629 \u0648\u062a\u062d\u062a\u0641\u0638 \u0628\u0627\u0644\u0646\u0635\u0641 \u0627\u0644\u0630\u064a \u064a\u0636\u0645\u0646 \u0627\u0633\u062a\u0645\u0631\u0627\u0631 \u0648\u062c\u0648\u062f \u0627\u0644\u062c\u0630\u0631 \u0648\u0641\u0642 \u0634\u0631\u0648\u0637 \u0627\u0644\u0637\u0631\u064a\u0642\u0629. \u0648\u062a\u062a\u0645\u064a\u0632 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0628\u0628\u0633\u0627\u0637\u062a\u0647\u0627 \u0648\u0636\u0645\u0627\u0646 \u062a\u0642\u0627\u0631\u0628\u0647\u0627 \u0641\u064a \u0627\u0644\u0638\u0631\u0648\u0641 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629\u060c \u0648\u0625\u0646 \u0643\u0627\u0646 \u062a\u0642\u0627\u0631\u0628\u0647\u0627 \u0623\u0628\u0637\u0623 \u0645\u0646 \u0628\u0639\u0636 \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0623\u062e\u0631\u0649. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Numerical_analysis\" title=\"7|Numerical analysis|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[7]<\/a><\/sup><\/p>\n<h2>\u0637\u0631\u064a\u0642\u0629 \u0646\u064a\u0648\u062a\u0646<\/h2>\n<p>\u0637\u0631\u064a\u0642\u0629 \u0646\u064a\u0648\u062a\u0646\u060c \u0623\u0648 \u0637\u0631\u064a\u0642\u0629 \u0646\u064a\u0648\u062a\u0646\u2013\u0631\u0627\u0641\u0633\u0648\u0646\u060c \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u062a\u0643\u0631\u0627\u0631\u064a\u0629 \u0644\u0625\u064a\u062c\u0627\u062f \u062c\u0630\u0648\u0631 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a. \u062a\u0628\u062f\u0623 \u0628\u062a\u062e\u0645\u064a\u0646 \u0623\u0648\u0644\u064a <i>x\u2080<\/i>\u060c \u062b\u0645 \u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0639\u0644\u0627\u0642\u0629:<\/p>\n<p><i>x\u2099\u208a\u2081=x\u2099\u2212f(x\u2099)\/f\u2032(x\u2099)<\/i><\/p>\n<p>\u0639\u0646\u062f\u0645\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0634\u0631\u0648\u0637 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0645\u062a\u062d\u0642\u0642\u0629 \u0648\u0644\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0645\u0642\u0627\u0645 \u0635\u0641\u0631\u0627\u064b. \u062a\u0642\u0648\u0645 \u0627\u0644\u0641\u0643\u0631\u0629 \u0639\u0644\u0649 \u0627\u0633\u062a\u0628\u062f\u0627\u0644 \u0627\u0644\u0645\u0646\u062d\u0646\u0649 \u0642\u0631\u0628 \u0627\u0644\u0646\u0642\u0637\u0629 \u0627\u0644\u062d\u0627\u0644\u064a\u0629 \u0628\u0645\u0645\u0627\u0633 \u0644\u0647\u060c \u062b\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062a\u0642\u0627\u0637\u0639 \u0627\u0644\u0645\u0645\u0627\u0633 \u0645\u0639 \u0645\u062d\u0648\u0631 <i>x<\/i> \u0628\u0648\u0635\u0641\u0647 \u062a\u062e\u0645\u064a\u0646\u0627\u064b \u062c\u062f\u064a\u062f\u0627\u064b.<\/p>\n<p>\u064a\u0645\u0643\u0646 \u0644\u0637\u0631\u064a\u0642\u0629 \u0646\u064a\u0648\u062a\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0634\u062f\u064a\u062f\u0629 \u0627\u0644\u0633\u0631\u0639\u0629 \u0628\u0627\u0644\u0642\u0631\u0628 \u0645\u0646 \u062c\u0630\u0631 \u0628\u0633\u064a\u0637 \u0639\u0646\u062f\u0645\u0627 \u062a\u062a\u0648\u0627\u0641\u0631 \u0634\u0631\u0648\u0637 \u0627\u0644\u0627\u0646\u062a\u0638\u0627\u0645 \u0648\u0627\u0644\u062a\u0642\u0627\u0631\u0628 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629\u060c \u0644\u0643\u0646 \u0627\u062e\u062a\u064a\u0627\u0631 \u0646\u0642\u0637\u0629 \u0627\u0644\u0628\u062f\u0627\u064a\u0629 \u0648\u0633\u0644\u0648\u0643 \u0627\u0644\u062f\u0627\u0644\u0629 \u0642\u062f \u064a\u0624\u062b\u0631\u0627\u0646 \u0628\u0635\u0648\u0631\u0629 \u0643\u0628\u064a\u0631\u0629 \u0641\u064a \u0646\u062c\u0627\u062d\u0647\u0627. \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0644\u0627 \u062a\u0642\u0627\u0633 \u0628\u0627\u0644\u0633\u0631\u0639\u0629 \u0641\u0642\u0637\u060c \u0628\u0644 \u0623\u064a\u0636\u0627\u064b \u0628\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0648\u0627\u0644\u0645\u0648\u062b\u0648\u0642\u064a\u0629 \u0648\u0646\u0637\u0627\u0642 \u0627\u0644\u062a\u0642\u0627\u0631\u0628. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Numerical_analysis\" title=\"8|Numerical analysis|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[8]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062d\u0630\u0641 \u0627\u0644\u063a\u0627\u0648\u0633\u064a<\/h2>\n<p>\u0627\u0644\u062d\u0630\u0641 \u0627\u0644\u063a\u0627\u0648\u0633\u064a \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u062d\u0644 \u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062e\u0637\u064a\u0629 \u0648\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0625\u0644\u0649 \u0635\u0648\u0631\u0629 \u0623\u0628\u0633\u0637. \u062a\u0639\u062a\u0645\u062f \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0639\u0644\u0649 \u0639\u0645\u0644\u064a\u0627\u062a \u0635\u0641\u064a\u0629 \u0623\u0648\u0644\u064a\u0629\u060c \u0645\u062b\u0644 \u062a\u0628\u062f\u064a\u0644 \u0635\u0641\u064a\u0646\u060c \u0648\u0636\u0631\u0628 \u0635\u0641 \u0641\u064a \u062b\u0627\u0628\u062a \u063a\u064a\u0631 \u0635\u0641\u0631\u064a\u060c \u0648\u0625\u0636\u0627\u0641\u0629 \u0645\u0636\u0627\u0639\u0641 \u0645\u0646 \u0635\u0641 \u0625\u0644\u0649 \u0635\u0641 \u0622\u062e\u0631.<\/p>\n<p>\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0644\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0627\u0644\u0635\u0648\u0631\u0629 \u0627\u0644\u0633\u0644\u0645\u064a\u0629 \u0644\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u062b\u0645 \u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062a\u0639\u0648\u064a\u0636 \u0627\u0644\u0639\u0643\u0633\u064a \u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u062d\u0644. \u0648\u062a\u0639\u062f \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0646 \u0627\u0644\u0623\u0633\u0627\u0644\u064a\u0628 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a \u0627\u0644\u0639\u062f\u062f\u064a\u060c \u0643\u0645\u0627 \u062a\u0634\u0643\u0644 \u0646\u0642\u0637\u0629 \u0627\u0646\u0637\u0644\u0627\u0642 \u0644\u0641\u0647\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0623\u0643\u062b\u0631 \u062a\u0637\u0648\u0631\u0627\u064b \u0644\u062d\u0644 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0643\u0628\u064a\u0631\u0629.<\/p>\n<h2>\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0648\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a<\/h2>\n<p>\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0647\u0648 \u0627\u0644\u0641\u0631\u0639 \u0627\u0644\u0630\u064a \u064a\u0647\u062a\u0645 \u0628\u0625\u064a\u062c\u0627\u062f \u062d\u0644\u0648\u0644 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0644\u0645\u0633\u0627\u0626\u0644 \u0642\u062f \u064a\u0643\u0648\u0646 \u062d\u0644\u0647\u0627 \u0627\u0644\u062f\u0642\u064a\u0642 \u063a\u064a\u0631 \u0645\u0645\u0643\u0646 \u0623\u0648 \u063a\u064a\u0631 \u0639\u0645\u0644\u064a \u062d\u0633\u0627\u0628\u064a\u0627\u064b\u060c \u0645\u0639 \u062f\u0631\u0627\u0633\u0629 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u062e\u0637\u0623 \u0648\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0648\u0633\u0631\u0639\u0629 \u0627\u0644\u062a\u0646\u0641\u064a\u0630. \u0648\u0644\u0630\u0644\u0643 \u062a\u0639\u062a\u0645\u062f \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0639\u0644\u0649 \u062a\u0635\u0645\u064a\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u062a\u0633\u062a\u0637\u064a\u0639 \u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0625\u0644\u0649 \u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u0646\u0641\u064a\u0630. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Numerical_analysis\" title=\"9|Numerical analysis|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[9]<\/a><\/sup><\/p>\n<p>\u0648\u062a\u0634\u0645\u0644 \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0643\u0627\u0645\u0644\u0627\u062a\u060c \u0648\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c \u0648\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629 \u0648\u0627\u0644\u0645\u062a\u062c\u0647\u0627\u062a \u0627\u0644\u0630\u0627\u062a\u064a\u0629\u060c \u0648\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u062d\u0644\u0648\u0644. \u0648\u0644\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0647\u062f\u0641 \u0641\u064a \u062c\u0645\u064a\u0639 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0645\u062c\u0631\u062f \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0631\u0642\u0645\u060c \u0628\u0644 \u0645\u0639\u0631\u0641\u0629 \u0645\u062f\u0649 \u062f\u0642\u062a\u0647 \u0648\u0645\u062f\u0649 \u062d\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0644\u0644\u0623\u062e\u0637\u0627\u0621.<\/p>\n<h2>\u0627\u0644\u062e\u0637\u0623 \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/h2>\n<p>\u0639\u0646\u062f\u0645\u0627 \u062a\u0646\u062a\u062c \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0642\u064a\u0645\u0629 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0646\u062a\u064a\u062c\u0629 \u062f\u0642\u064a\u0642\u0629\u060c \u064a\u062c\u0628 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062e\u0637\u0623. \u0648\u064a\u064f\u0645\u064a\u0632 \u0639\u0627\u062f\u0629 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u0645\u0637\u0644\u0642 \u0648\u0627\u0644\u062e\u0637\u0623 \u0627\u0644\u0646\u0633\u0628\u064a\u060c \u0643\u0645\u0627 \u062a\u062f\u0631\u0633 \u0623\u062e\u0637\u0627\u0621 \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0639\u0646 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u062f\u0627\u062e\u0644 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u060c \u0648\u0623\u062e\u0637\u0627\u0621 \u0627\u0644\u0642\u0637\u0639 \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0639\u0646 \u0625\u064a\u0642\u0627\u0641 \u0639\u0645\u0644\u064a\u0629 \u0644\u0627 \u0646\u0647\u0627\u0626\u064a\u0629 \u0628\u0639\u062f \u0639\u062f\u062f \u0645\u062d\u062f\u0648\u062f \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a.<\/p>\n<p>\u0648\u0644\u0647\u0630\u0627 \u0641\u0625\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062c\u064a\u062f\u0629 \u0644\u0627 \u062a\u0628\u062d\u062b \u0641\u0642\u0637 \u0639\u0646 \u0639\u062f\u062f \u0642\u0644\u064a\u0644 \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a\u060c \u0628\u0644 \u064a\u0646\u0628\u063a\u064a \u0623\u0646 \u062a\u062d\u0642\u0642 \u062a\u0648\u0627\u0632\u0646\u0627\u064b \u0628\u064a\u0646 \u0627\u0644\u062f\u0642\u0629 \u0648\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0648\u0627\u0644\u0643\u0641\u0627\u0621\u0629. \u0648\u064a\u0624\u0643\u062f \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0623\u0646 \u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u064a\u062a\u0637\u0644\u0628 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062e\u0637\u0623 \u0648\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0648\u0633\u0631\u0639\u0629 \u0627\u0644\u062a\u0646\u0641\u064a\u0630 \u0648\u0645\u0644\u0627\u0621\u0645\u0629 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0644\u0644\u0645\u0633\u0623\u0644\u0629. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Numerical_analysis\" title=\"10|Numerical analysis|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[10]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062a\u0643\u0631\u0627\u0631 \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629<\/h2>\n<p>\u062a\u0639\u062a\u0645\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0643\u062b\u064a\u0631\u0629 \u0639\u0644\u0649 \u062a\u0643\u0631\u0627\u0631 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0646\u0641\u0633\u0647\u0627. \u0641\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0644\u062f\u064a\u0646\u0627 \u0642\u064a\u0645\u0629 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 <i>x\u2080<\/i>\u060c \u064a\u0645\u0643\u0646 \u0625\u0646\u062a\u0627\u062c \u0633\u0644\u0633\u0644\u0629 <i>x\u2081,x\u2082,x\u2083,&#8230;<\/i> \u0648\u0641\u0642 \u0642\u0627\u0639\u062f\u0629 \u0645\u0639\u064a\u0646\u0629\u060c \u0639\u0644\u0649 \u0623\u0645\u0644 \u0623\u0646 \u062a\u0642\u062a\u0631\u0628 \u0627\u0644\u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u062d\u0644 \u0627\u0644\u0645\u0637\u0644\u0648\u0628.<\/p>\n<p>\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <i>x\u2099\u2192x*<\/i> \u0639\u0646\u062f\u0645\u0627 \u064a\u0632\u062f\u0627\u062f <i>n<\/i>\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0642\u0648\u0644 \u0625\u0646 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u062a\u062a\u0642\u0627\u0631\u0628 \u0625\u0644\u0649 \u0627\u0644\u062d\u0644 <i>x*<\/i>\u060c \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0647\u0630\u0627 \u0627\u0644\u062a\u0641\u0633\u064a\u0631 \u0645\u0646\u0627\u0633\u0628\u0627\u064b \u0644\u0644\u0645\u0633\u0623\u0644\u0629. \u0648\u0645\u0646 \u0647\u0646\u0627 \u062a\u0638\u0647\u0631 \u0645\u0641\u0627\u0647\u064a\u0645 \u0645\u0639\u062f\u0644 \u0627\u0644\u062a\u0642\u0627\u0631\u0628\u060c \u0648\u0634\u0631\u0648\u0637 \u0627\u0644\u062a\u0642\u0627\u0631\u0628\u060c \u0648\u0645\u062c\u0627\u0644 \u0627\u0644\u062a\u0642\u0627\u0631\u0628.<\/p>\n<h2>\u062a\u0633\u0631\u064a\u0639 \u0627\u0644\u062a\u0642\u0627\u0631\u0628<\/h2>\n<p>\u0642\u062f \u062a\u0646\u062a\u062c \u0628\u0639\u0636 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0645\u062a\u062a\u0627\u0644\u064a\u0627\u062a \u062a\u0642\u062a\u0631\u0628 \u0645\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0628\u0628\u0637\u0621. \u0648\u0644\u0630\u0644\u0643 \u0637\u0648\u0631\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0637\u0631\u0642\u0627\u064b \u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0645\u062a\u062a\u0627\u0644\u064a\u0627\u062a \u0625\u0644\u0649 \u0645\u062a\u062a\u0627\u0644\u064a\u0627\u062a \u0623\u062e\u0631\u0649 \u062a\u062a\u0642\u0627\u0631\u0628 \u0628\u0635\u0648\u0631\u0629 \u0623\u0633\u0631\u0639. \u0648\u062a\u0648\u0636\u062d \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0621 \u0627\u0644\u062e\u0627\u0631\u062c\u064a \u0623\u0646 \u0628\u0639\u0636 \u0627\u0644\u062a\u062d\u0648\u064a\u0644\u0627\u062a \u062a\u0647\u062f\u0641 \u0625\u0644\u0649 \u062a\u0633\u0631\u064a\u0639 \u062a\u0642\u0627\u0631\u0628 \u0645\u062a\u062a\u0627\u0644\u064a\u0629 <i>S\u2099<\/i> \u0646\u062d\u0648 \u062d\u062f\u0647\u0627 <i>S<\/i> \u0645\u0639 \u0627\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u0649 \u0627\u0644\u062d\u062f \u0646\u0641\u0633\u0647. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Extrapolation_algorithm\" title=\"11|Extrapolation algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[11]<\/a><\/sup><\/p>\n<h2>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u0639\u062f\u062f\u064a<\/h2>\n<p>\u0639\u0646\u062f\u0645\u0627 \u064a\u0635\u0639\u0628 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0628\u0635\u0648\u0631\u0629 \u062a\u062d\u0644\u064a\u0644\u064a\u0629\u060c \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0639\u062f\u062f\u064a\u0629 \u0644\u062a\u0642\u0631\u064a\u0628\u0647. \u0645\u0646 \u0623\u0634\u0647\u0631\u0647\u0627 \u0642\u0627\u0639\u062f\u0629 \u0634\u0628\u0647 \u0627\u0644\u0645\u0646\u062d\u0631\u0641 \u0648\u0642\u0627\u0639\u062f\u0629 \u0633\u0645\u0628\u0633\u0648\u0646\u060c \u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0637\u0631\u0642 \u0623\u0643\u062b\u0631 \u062a\u0642\u062f\u0645\u0627\u064b \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0645\u062c\u0627\u0644 \u0623\u0648 \u0627\u062e\u062a\u064a\u0627\u0631 \u0646\u0642\u0627\u0637 \u062a\u0642\u064a\u064a\u0645 \u0645\u0646\u0627\u0633\u0628\u0629.<\/p>\n<p>\u062a\u0646\u062a\u062c \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u0642 \u062a\u0642\u0631\u064a\u0628\u0627\u064b \u0644\u0644\u062a\u0643\u0627\u0645\u0644 \u0645\u0639 \u062d\u062f \u0644\u0644\u062e\u0637\u0623 \u064a\u0645\u0643\u0646 \u062a\u0642\u062f\u064a\u0631\u0647 \u0641\u064a \u0638\u0631\u0648\u0641 \u0645\u0639\u064a\u0646\u0629. \u0648\u064a\u0639\u062a\u0645\u062f \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u0644\u0649 \u0637\u0628\u064a\u0639\u0629 \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0648\u0646\u0637\u0627\u0642 \u0627\u0644\u062a\u0643\u0627\u0645\u0644\u060c \u0648\u0627\u0644\u062f\u0642\u0629 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629\u060c \u0648\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062d\u0633\u0627\u0628.<\/p>\n<h2>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u062d\u0644 \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0639\u062f\u062f\u064a\u0627\u064b \u0639\u0646\u062f\u0645\u0627 \u0644\u0627 \u064a\u062a\u0648\u0627\u0641\u0631 \u062d\u0644 \u062a\u062d\u0644\u064a\u0644\u064a \u0639\u0645\u0644\u064a. \u0648\u0645\u0646 \u0623\u0634\u0647\u0631 \u0627\u0644\u0637\u0631\u0642 \u0637\u0631\u064a\u0642\u0629 \u0623\u0648\u064a\u0644\u0631 \u0648\u0637\u0631\u0642 \u0631\u0648\u0646\u063a\u0647\u2013\u0643\u0648\u062a\u0627 \u0648\u0637\u0631\u0642 \u0627\u0644\u0641\u0631\u0648\u0642 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0648\u0627\u0644\u0639\u0646\u0627\u0635\u0631 \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0641\u064a \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629.<\/p>\n<p>\u062a\u0642\u0648\u0645 \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0639\u0627\u0645\u0629 \u0641\u064a \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0632\u0645\u0646\u064a\u0629 \u0639\u0644\u0649 \u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u062a\u0637\u0648\u0631 \u0627\u0644\u0645\u0633\u062a\u0645\u0631 \u0625\u0644\u0649 \u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u0645\u0646\u0641\u0635\u0644\u0629. \u0648\u064a\u0635\u0628\u062d \u0627\u062e\u062a\u064a\u0627\u0631 \u062d\u062c\u0645 \u0627\u0644\u062e\u0637\u0648\u0629 \u0645\u0647\u0645\u0627\u064b \u062c\u062f\u0627\u064b\u061b \u0641\u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0642\u062f \u062a\u0624\u062f\u064a \u0625\u0644\u0649 \u062e\u0637\u0623 \u0643\u0628\u064a\u0631 \u0623\u0648 \u0625\u0644\u0649 \u0639\u062f\u0645 \u0627\u0633\u062a\u0642\u0631\u0627\u0631\u060c \u0628\u064a\u0646\u0645\u0627 \u062a\u0632\u064a\u062f \u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u0639\u062f\u062f \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u064a \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a<\/h2>\n<p>\u064a\u0634\u0643\u0644 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a \u0623\u062d\u062f \u0623\u0643\u0628\u0631 \u0645\u064a\u0627\u062f\u064a\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629. \u0641\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u062a\u0638\u0647\u0631 \u0641\u064a \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u062e\u0637\u064a\u0629\u060c \u0648\u0627\u0644\u062a\u062d\u0648\u064a\u0644\u0627\u062a\u060c \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629\u060c \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629. \u0648\u062a\u0634\u0645\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u062d\u0630\u0641 \u0627\u0644\u063a\u0627\u0648\u0633\u064a\u060c \u0648\u062a\u062d\u0644\u064a\u0644 <i>LU<\/i>\u060c \u0648\u062a\u062d\u0644\u064a\u0644 <i>QR<\/i>\u060c \u0648\u0637\u0631\u0642 \u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629.<\/p>\n<p>\u0623\u0635\u0628\u062d\u062a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0633\u0631\u064a\u0639\u0629 \u0641\u064a \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a \u0645\u0646 \u0623\u0647\u0645 \u0627\u0644\u0623\u062f\u0648\u0627\u062a \u0641\u064a \u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629\u060c \u0644\u0623\u0646 \u062d\u062c\u0645 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u0629 \u0641\u064a \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629 \u0642\u062f \u064a\u0643\u0648\u0646 \u0636\u062e\u0645\u0627\u064b \u062c\u062f\u0627\u064b\u060c \u0645\u0645\u0627 \u064a\u062c\u0639\u0644 \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0641\u0639\u0627\u0644\u0629 \u0648\u0623\u062e\u0631\u0649 \u0628\u0637\u064a\u0626\u0629 \u0641\u0631\u0642\u0627\u064b \u0639\u0645\u0644\u064a\u0627\u064b \u0647\u0627\u0626\u0644\u0627\u064b.<\/p>\n<h2>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 QR<\/h2>\n<p>\u062a\u0639\u062a\u0645\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 <i>QR<\/i> \u0639\u0644\u0649 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0625\u0644\u0649 \u062d\u0627\u0635\u0644 \u0636\u0631\u0628 \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u062a\u0639\u0627\u0645\u062f\u0629 \u0623\u0648 \u0648\u062d\u062f\u0648\u064a\u0629 \u0648\u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u062b\u0644\u062b\u064a\u0629 \u0639\u0644\u0648\u064a\u0629. \u0648\u062a\u0633\u062a\u062e\u062f\u0645 \u0641\u064a \u0645\u0633\u0627\u0626\u0644 \u0639\u062f\u064a\u062f\u0629 \u0645\u0646 \u0628\u064a\u0646\u0647\u0627 \u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629.<\/p>\n<p>\u0648\u0642\u062f \u0623\u0635\u0628\u062d\u062a \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u062d\u0633\u0627\u0628 \u0627\u0644\u0623\u0646\u0638\u0645\u0629 \u0648\u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0630\u0627\u062a\u064a\u0629 \u062c\u0632\u0621\u0627\u064b \u0645\u0647\u0645\u0627\u064b \u0645\u0646 \u062a\u0637\u0648\u0631 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0627\u0644\u062d\u062f\u064a\u062b\u060c \u0648\u062a\u0630\u0643\u0631 \u0627\u0644\u0623\u062f\u0628\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0623\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 <i>QR<\/i> \u0643\u0627\u0646\u062a \u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u0623\u062b\u0631\u062a \u0628\u0635\u0648\u0631\u0629 \u0643\u0628\u064a\u0631\u0629 \u0641\u064a \u062a\u0637\u0648\u064a\u0631 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b\u0629. <sup class=\"ref\"><a href=\"https:\/\/www.ams.org\/bull\/2012-49-04\/S0273-0979-2012-01379-4\/S0273-0979-2012-01379-4.pdf\" title=\"12|Numerical algorithms and the development of computational mathematics|Eitan Tadmor, Bulletin of the American Mathematical Society|2012\" target=\"_blank\" rel=\"noopener\">[12]<\/a><\/sup><\/p>\n<h2>\u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0633\u0631\u064a\u0639<\/h2>\n<p>\u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0633\u0631\u064a\u0639\u060c \u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0627\u062e\u062a\u0635\u0627\u0631\u0627\u064b \u0628\u0640FFT\u060c \u0647\u0648 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0641\u0639\u0627\u0644\u0629 \u0644\u062d\u0633\u0627\u0628 \u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0645\u062a\u0642\u0637\u0639. \u0648\u062a\u0643\u0645\u0646 \u0623\u0647\u0645\u064a\u062a\u0647 \u0641\u064a \u0623\u0646\u0647 \u064a\u0633\u062a\u063a\u0644 \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u0644\u062a\u062d\u0648\u064a\u0644 \u0644\u062a\u0642\u0644\u064a\u0644 \u0639\u062f\u062f \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629 \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u0627\u0644\u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0645\u0628\u0627\u0634\u0631 \u0644\u0644\u0635\u064a\u063a\u0629.<\/p>\n<p>\u0623\u0635\u0628\u062d FFT \u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0625\u0634\u0627\u0631\u0627\u062a \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0639\u0644\u0645\u064a\u060c \u0648\u062a\u0635\u0641 \u0627\u0644\u0623\u062f\u0628\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u062a\u0627\u0631\u064a\u062e\u064a\u0627\u064b \u0638\u0647\u0648\u0631\u0647 \u0641\u064a \u0633\u062a\u064a\u0646\u064a\u0627\u062a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u0639\u0634\u0631\u064a\u0646 \u0628\u0648\u0635\u0641\u0647 \u0623\u062d\u062f \u0627\u0644\u062a\u0637\u0648\u0631\u0627\u062a \u0627\u0644\u062a\u064a \u0643\u0627\u0646 \u0644\u0647\u0627 \u0623\u062b\u0631 \u0643\u0628\u064a\u0631 \u0641\u064a \u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0637\u064a\u0641\u064a\u0629 \u0648\u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0639\u0644\u0645\u064a\u0629. <sup class=\"ref\"><a href=\"https:\/\/www.ams.org\/bull\/2012-49-04\/S0273-0979-2012-01379-4\/S0273-0979-2012-01379-4.pdf\" title=\"13|Numerical algorithms and the development of computational mathematics|Eitan Tadmor, Bulletin of the American Mathematical Society|2012\" target=\"_blank\" rel=\"noopener\">[13]<\/a><\/sup><\/p>\n<p>\u0648\u062a\u0631\u062c\u0639 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 Cooley\u2013Tukey \u0627\u0644\u062d\u062f\u064a\u062b\u0629 \u0625\u0644\u0649 \u0648\u0631\u0642\u0629 \u0628\u062d\u062b\u064a\u0629 \u0634\u0647\u064a\u0631\u0629 \u0646\u0634\u0631\u0647\u0627 \u062c\u064a\u0645\u0633 \u0643\u0648\u0644\u064a \u0648\u062c\u0648\u0646 \u062a\u0648\u0643\u064a \u0639\u0627\u0645 1965\u060c \u0648\u0642\u062f \u0633\u0627\u0647\u0645\u062a \u0641\u064a \u062c\u0639\u0644 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0633\u0631\u064a\u0639 \u0644\u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0645\u062a\u0642\u0637\u0639 \u0639\u0645\u0644\u064a\u0627\u064b \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639.<\/p>\n<h2>\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u062d\u0633\u0627\u0628\u064a<\/h2>\n<p>\u0644\u0627 \u064a\u0643\u0641\u064a \u0623\u0646 \u062a\u0643\u0648\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0635\u062d\u064a\u062d\u0629\u061b \u0625\u0630 \u064a\u062c\u0628 \u0645\u0639\u0631\u0641\u0629 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062a\u064a \u062a\u062d\u062a\u0627\u062c\u0647\u0627. \u0648\u064a\u0634\u064a\u0631 \u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u0625\u0644\u0649 \u062f\u0631\u0627\u0633\u0629 \u0646\u0645\u0648 \u0639\u062f\u062f \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0623\u0648 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0630\u0627\u0643\u0631\u0629 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629 \u0645\u0639 \u0627\u0632\u062f\u064a\u0627\u062f \u062d\u062c\u0645 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a.<\/p>\n<p>\u0625\u0630\u0627 \u0643\u0627\u0646 \u062d\u062c\u0645 \u0627\u0644\u0645\u062f\u062e\u0644 <i>n<\/i>\u060c \u0641\u0642\u062f \u062a\u062d\u062a\u0627\u062c \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0639\u064a\u0646\u0629 \u0625\u0644\u0649 \u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u064a\u062a\u0646\u0627\u0633\u0628 \u062a\u0642\u0631\u064a\u0628\u0627\u064b \u0645\u0639 <i>n<\/i>\u060c \u0628\u064a\u0646\u0645\u0627 \u062a\u062d\u062a\u0627\u062c \u0623\u062e\u0631\u0649 \u0625\u0644\u0649 \u0639\u062f\u062f \u064a\u062a\u0646\u0627\u0633\u0628 \u0645\u0639 <i>n\u00b2<\/i> \u0623\u0648 <i>n\u00b3<\/i> \u0623\u0648 \u0623\u0643\u0628\u0631. \u0648\u0644\u0647\u0630\u0627 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0639\u0645\u0644 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u062a\u0627\u0646 \u0628\u0635\u0648\u0631\u0629 \u0645\u0642\u0628\u0648\u0644\u0629 \u0639\u0644\u0649 \u0645\u0633\u0627\u0626\u0644 \u0635\u063a\u064a\u0631\u0629\u060c \u0644\u0643\u0646 \u0625\u062d\u062f\u0627\u0647\u0645\u0627 \u0642\u062f \u062a\u0635\u0628\u062d \u063a\u064a\u0631 \u0639\u0645\u0644\u064a\u0629 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0628\u0631 \u062d\u062c\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/p>\n<h2>\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0632\u0645\u0646\u064a<\/h2>\n<p>\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0632\u0645\u0646\u064a \u064a\u0642\u064a\u0633 \u0643\u064a\u0641\u064a\u0629 \u0646\u0645\u0648 \u0639\u062f\u062f \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0645\u0639 \u062d\u062c\u0645 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a. \u0648\u064a\u0633\u062a\u062e\u062f\u0645 \u0639\u0644\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0639\u0627\u062f\u0629 \u062a\u0631\u0645\u064a\u0632\u0627\u064b \u0645\u062b\u0644 <i>O(n)<\/i> \u0648<i>O(n\u00b2)<\/i> \u0648<i>O(log n)<\/i> \u0644\u0648\u0635\u0641 \u0645\u0639\u062f\u0644 \u0627\u0644\u0646\u0645\u0648 \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u064a.<\/p>\n<p>\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u0645\u062b\u0627\u0644 \u0645\u0647\u0645 \u0639\u0644\u0649 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0646\u0645\u0648 \u0643\u0641\u0627\u0621\u062a\u0647\u0627 \u0628\u0635\u0648\u0631\u0629 \u062c\u064a\u062f\u0629 \u062c\u062f\u0627\u064b \u0645\u0639 \u062d\u062c\u0645 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a\u061b \u0625\u0630 \u0625\u0646 \u0639\u062f\u062f \u062e\u0637\u0648\u0627\u062a\u0647\u0627 \u0645\u062d\u062f\u0648\u062f \u0628\u0646\u0645\u0648 \u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a \u062a\u0642\u0631\u064a\u0628\u0627\u064b \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0625\u0644\u0649 \u0642\u064a\u0645\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0645\u0639 \u0627\u062e\u062a\u0644\u0627\u0641 \u0627\u0644\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u062f\u0642\u064a\u0642\u0629 \u0628\u062d\u0633\u0628 \u0637\u0631\u064a\u0642\u0629 \u0642\u064a\u0627\u0633 \u062d\u062c\u0645 \u0627\u0644\u0645\u062f\u062e\u0644. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Euclidean_algorithm\" title=\"14|Euclidean algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[14]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0627\u0644\u0645\u0643\u0627\u0646\u064a<\/h2>\n<p>\u0625\u0644\u0649 \u062c\u0627\u0646\u0628 \u0627\u0644\u0632\u0645\u0646\u060c \u0642\u062f \u062a\u062d\u062a\u0627\u062c \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0644\u0649 \u0645\u0633\u0627\u062d\u0629 \u0641\u064a \u0627\u0644\u0630\u0627\u0643\u0631\u0629 \u0644\u062a\u062e\u0632\u064a\u0646 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0648\u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0648\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0648\u0633\u064a\u0637\u0629. \u0648\u062a\u0635\u0628\u062d \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0645\u0647\u0645\u0629 \u062e\u0635\u0648\u0635\u0627\u064b \u0639\u0646\u062f \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0636\u062e\u0645\u0629 \u0623\u0648 \u0634\u0628\u0643\u0627\u062a \u0639\u062f\u062f\u064a\u0629 \u0623\u0648 \u0628\u064a\u0627\u0646\u0627\u062a \u0639\u0627\u0644\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f.<\/p>\n<p>\u0648\u0642\u062f \u062a\u0643\u0648\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0623\u0633\u0631\u0639 \u0644\u0643\u0646\u0647\u0627 \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0630\u0627\u0643\u0631\u0629 \u0623\u0643\u0628\u0631\u060c \u0628\u064a\u0646\u0645\u0627 \u0642\u062f \u062a\u0643\u0648\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0623\u062e\u0631\u0649 \u0623\u0628\u0637\u0623 \u0644\u0643\u0646\u0647\u0627 \u062a\u0639\u0645\u0644 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0633\u0627\u062d\u0629 \u0645\u062d\u062f\u0648\u062f\u0629. \u0648\u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u0627\u062e\u062a\u064a\u0627\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0637\u0628\u064a\u0639\u0629 \u0627\u0644\u0646\u0638\u0627\u0645 \u0648\u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u0645\u062a\u0627\u062d\u0629\u060c \u0648\u0644\u064a\u0633 \u0639\u0644\u0649 \u0633\u0631\u0639\u0629 \u0627\u0644\u062a\u0646\u0641\u064a\u0630 \u0648\u062d\u062f\u0647\u0627.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062f\u0642\u064a\u0642\u0629 \u0648\u0627\u0644\u062a\u0642\u0631\u064a\u0628\u064a\u0629<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0645\u064a\u064a\u0632 \u0628\u064a\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0646\u062a\u062c \u0646\u062a\u064a\u062c\u0629 \u062f\u0642\u064a\u0642\u0629 \u0636\u0645\u0646 \u0646\u0645\u0648\u0630\u062c \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645 \u0648\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0646\u062a\u062c \u062a\u0642\u0631\u064a\u0628\u0627\u064b. \u0641\u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0635\u062d\u064a\u062d\u060c \u064a\u0645\u0643\u0646 \u0645\u062b\u0644\u0627\u064b \u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u0623\u0646 \u062a\u0639\u0637\u064a \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631 \u0628\u0635\u0648\u0631\u0629 \u062f\u0642\u064a\u0642\u0629. \u0623\u0645\u0627 \u0641\u064a \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0641\u0642\u062f \u062a\u0643\u0648\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u062a\u0642\u0631\u064a\u0628\u0627\u064b \u0628\u0633\u0628\u0628 \u0637\u0628\u064a\u0639\u0629 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0623\u0648 \u0628\u0633\u0628\u0628 \u062a\u0645\u062b\u064a\u0644 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u062d\u0642\u064a\u0642\u064a\u0629 \u0641\u064a \u0627\u0644\u062d\u0627\u0633\u0648\u0628.<\/p>\n<p>\u0644\u0627 \u064a\u0639\u0646\u064a \u0627\u0644\u062a\u0642\u0631\u064a\u0628 \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u0636\u0639\u0641 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629\u061b \u0641\u0641\u064a \u0645\u0633\u0627\u0626\u0644 \u0643\u062b\u064a\u0631\u0629 \u0644\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u062d\u0644 \u0627\u0644\u062f\u0642\u064a\u0642 \u0639\u0645\u0644\u064a\u0627\u064b\u060c \u0628\u064a\u0646\u0645\u0627 \u064a\u0645\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062a\u0642\u0631\u064a\u0628 \u0630\u064a \u062e\u0637\u0623 \u0645\u0636\u0628\u0648\u0637 \u0648\u0635\u063a\u064a\u0631 \u062c\u062f\u0627\u064b. \u0648\u0647\u0630\u0627 \u0647\u0648 \u062c\u0648\u0647\u0631 \u0643\u062b\u064a\u0631 \u0645\u0646 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Numerical_analysis\" title=\"15|Numerical analysis|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[15]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062d\u062a\u0645\u064a\u0629<\/h2>\n<p>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062d\u062a\u0645\u064a\u0629 \u0647\u064a \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0627\u0644\u062e\u0637\u0648\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0635\u0648\u0631\u0629 \u0643\u0627\u0645\u0644\u0629 \u0645\u0646 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u062d\u0627\u0644\u064a\u0629 \u0648\u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a\u060c \u0628\u062d\u064a\u062b \u064a\u0624\u062f\u064a \u062a\u0634\u063a\u064a\u0644\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u062f\u062e\u0644 \u0646\u0641\u0633\u0647 \u0648\u0641\u0642 \u0627\u0644\u0634\u0631\u0648\u0637 \u0646\u0641\u0633\u0647\u0627 \u0625\u0644\u0649 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0646\u0641\u0633\u0647\u0627. \u0645\u0639\u0638\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0643\u0644\u0627\u0633\u064a\u0643\u064a\u0629\u060c \u0645\u062b\u0644 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u0648\u0627\u0644\u062d\u0630\u0641 \u0627\u0644\u063a\u0627\u0648\u0633\u064a\u060c \u0630\u0627\u062a \u0637\u0628\u064a\u0639\u0629 \u062d\u062a\u0645\u064a\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629<\/h2>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 \u0628\u0639\u0636 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0623\u0648 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0645\u0635\u062f\u0631\u0627\u064b \u0645\u0646 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0623\u062b\u0646\u0627\u0621 \u0627\u0644\u062a\u0646\u0641\u064a\u0630. \u0648\u0642\u062f \u064a\u0643\u0648\u0646 \u0627\u0644\u0647\u062f\u0641 \u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0623\u062f\u0627\u0621 \u0623\u0648 \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u0633\u0627\u0626\u0644 \u0643\u0628\u064a\u0631\u0629 \u0623\u0648 \u0628\u0646\u0627\u0621 \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629.<\/p>\n<p>\u062a\u0638\u0647\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0648\u0627\u0644\u062d\u0648\u0633\u0628\u0629\u060c \u0648\u0641\u064a \u0637\u0631\u0642 \u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629\u060c \u0648\u0641\u064a \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0645\u0648\u0646\u062a \u0643\u0627\u0631\u0644\u0648. \u0648\u062a\u062a\u0645\u064a\u0632 \u0647\u0630\u0647 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0628\u0623\u0646 \u062a\u062d\u0644\u064a\u0644\u0647\u0627 \u0642\u062f \u064a\u062a\u0636\u0645\u0646 \u0627\u062d\u062a\u0645\u0627\u0644 \u0646\u062c\u0627\u062d \u0623\u0648 \u062a\u0648\u0642\u0639\u0627\u064b \u0644\u0632\u0645\u0646 \u0627\u0644\u062a\u0646\u0641\u064a\u0630\u060c \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0646\u062a\u064a\u062c\u0629 \u062d\u062a\u0645\u064a\u0629 \u0641\u064a \u0643\u0644 \u062a\u0634\u063a\u064a\u0644.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u064a\u0629 \u0648\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0639\u0648\u062f\u064a\u0629<\/h2>\n<p>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u064a\u0629 \u062a\u0646\u0641\u0630 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0645\u0631\u0627\u0631\u0627\u064b \u062d\u062a\u0649 \u064a\u062a\u062d\u0642\u0642 \u0634\u0631\u0637 \u062a\u0648\u0642\u0641. \u0623\u0645\u0627 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0639\u0648\u062f\u064a\u0629 \u0641\u062a\u0639\u0631\u0651\u0641 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u062c\u0632\u0626\u064a\u0627\u064b \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0627\u0644\u0627\u062a \u0623\u0635\u063a\u0631 \u0645\u0646 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0646\u0641\u0633\u0647\u0627\u060c \u062b\u0645 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u062d\u0627\u0644\u0629 \u0623\u0633\u0627\u0633 \u0644\u0625\u0646\u0647\u0627\u0621 \u0627\u0644\u0639\u0645\u0644\u064a\u0629.<\/p>\n<p>\u062a\u0638\u0647\u0631 \u0627\u0644\u0639\u0648\u062f\u064a\u0629 \u0628\u0635\u0648\u0631\u0629 \u0637\u0628\u064a\u0639\u064a\u0629 \u0641\u064a \u0645\u0633\u0627\u0626\u0644 \u0645\u062b\u0644 \u0627\u0644\u0645\u062a\u062a\u0627\u0644\u064a\u0627\u062a\u060c \u0648\u062a\u0642\u0633\u064a\u0645 \u0627\u0644\u0645\u0633\u0627\u0626\u0644\u060c \u0648\u0628\u0646\u0649 \u0627\u0644\u0623\u0634\u062c\u0627\u0631. \u0648\u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629\u060c \u062a\u0631\u062a\u0628\u0637 \u0635\u062d\u0629 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0639\u0648\u062f\u064a\u0629 \u063a\u0627\u0644\u0628\u0627\u064b \u0628\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0621 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u061b \u0625\u0630 \u064a\u0645\u0643\u0646 \u0625\u062b\u0628\u0627\u062a \u0635\u062d\u0629 \u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0633\u0627\u0633 \u062b\u0645 \u0625\u062b\u0628\u0627\u062a \u0623\u0646 \u0635\u062d\u0629 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0635\u063a\u0631 \u062a\u0624\u062f\u064a \u0625\u0644\u0649 \u0635\u062d\u0629 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0643\u0628\u0631.<\/p>\n<h2>\u0634\u0631\u0637 \u0627\u0644\u062a\u0648\u0642\u0641<\/h2>\n<p>\u0645\u0646 \u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0648\u062c\u0648\u062f \u0634\u0631\u0637 \u0648\u0627\u0636\u062d \u0644\u0644\u062a\u0648\u0642\u0641 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0630\u0644\u0643 \u0645\u0637\u0644\u0648\u0628\u0627\u064b. \u0641\u0625\u0630\u0627 \u0627\u0633\u062a\u0645\u0631\u062a \u0627\u0644\u0639\u0645\u0644\u064a\u0629 \u0625\u0644\u0649 \u0645\u0627 \u0644\u0627 \u0646\u0647\u0627\u064a\u0629 \u062f\u0648\u0646 \u0625\u0646\u062a\u0627\u062c \u0646\u062a\u064a\u062c\u0629\u060c \u0641\u0644\u0627 \u062a\u0643\u0648\u0646 \u0642\u062f \u062d\u0644\u062a \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0636\u0645\u0646 \u0627\u0644\u0645\u0639\u0646\u0649 \u0627\u0644\u0645\u0637\u0644\u0648\u0628.<\/p>\n<p>\u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u062a\u0648\u062c\u062f \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0623\u0648 \u0639\u0645\u0644\u064a\u0627\u062a \u0642\u062f \u0644\u0627 \u062a\u062a\u0648\u0642\u0641 \u0639\u0644\u0649 \u0628\u0639\u0636 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a. \u0648\u062a\u0639\u062f \u0645\u0633\u0623\u0644\u0629 \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0639\u0645\u0644\u064a\u0629 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0633\u062a\u062a\u0648\u0642\u0641 \u0639\u0644\u0649 \u0645\u062f\u062e\u0644 \u0645\u0639\u064a\u0646 \u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0639\u0645\u064a\u0642\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062d\u0633\u0627\u0628\u060c \u0648\u062a\u0631\u062a\u0628\u0637 \u0628\u0645\u0634\u0643\u0644\u0629 \u0627\u0644\u062a\u0648\u0642\u0641 \u0627\u0644\u062a\u064a \u062a\u0639\u062f \u0645\u0646 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0627\u0644\u0646\u0638\u0631\u064a\u0629. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Algorithm\" title=\"16|Algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[16]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0627\u0644\u0646\u0645\u0630\u062c\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629<\/h2>\n<p>\u062a\u0628\u062f\u0623 \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0628\u0646\u0645\u0648\u0630\u062c \u0631\u064a\u0627\u0636\u064a\u060c \u062b\u0645 \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0644\u062a\u062d\u0648\u064a\u0644 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0625\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062d\u0633\u0627\u0628. \u0641\u0642\u062f \u064a\u0635\u0641 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u062a\u063a\u064a\u0631 \u062f\u0631\u062c\u0629 \u0627\u0644\u062d\u0631\u0627\u0631\u0629 \u0628\u0645\u0639\u0627\u062f\u0644\u0629 \u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c \u0644\u0643\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0642\u064a\u0645 \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u0639\u0646\u062f \u0646\u0642\u0627\u0637 \u0632\u0645\u0646\u064a\u0629 \u0645\u062d\u062f\u062f\u0629 \u064a\u062a\u0637\u0644\u0628 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u062f\u062f\u064a\u0629.<\/p>\n<p>\u0648\u0647\u0630\u0627 \u064a\u0648\u0636\u062d \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0648\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629: \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u064a\u0635\u0641 \u0627\u0644\u0638\u0627\u0647\u0631\u0629 \u0623\u0648 \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629\u060c \u0628\u064a\u0646\u0645\u0627 \u062a\u062d\u062f\u062f \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0637\u0631\u064a\u0642\u0629 \u062d\u0633\u0627\u0628\u064a\u0629 \u0644\u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0648\u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0645\u0646\u0647.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u064a \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629<\/h2>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0644\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0627\u0644\u0646\u0642\u0627\u0637 \u0648\u0627\u0644\u062e\u0637\u0648\u0637 \u0648\u0627\u0644\u0645\u0646\u062d\u0646\u064a\u0627\u062a \u0648\u0627\u0644\u0645\u0636\u0644\u0639\u0627\u062a \u0648\u0627\u0644\u0623\u0633\u0637\u062d. \u0648\u062a\u0634\u0645\u0644 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0633\u0627\u0641\u0627\u062a \u0648\u0627\u0644\u062a\u0642\u0627\u0637\u0639\u0627\u062a\u060c \u0648\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0648\u0627\u0636\u0639\u060c \u0648\u0628\u0646\u0627\u0621 \u0627\u0644\u0647\u064a\u0627\u0643\u0644 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u0629\u060c \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0623\u0634\u0643\u0627\u0644.<\/p>\n<p>\u0648\u062a\u0631\u062a\u0628\u0637 \u0647\u0630\u0647 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0628\u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0627\u0644\u062a\u062d\u0644\u064a\u0644\u064a\u0629 \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0631\u0633\u0648\u0645\u060c \u0643\u0645\u0627 \u062a\u0633\u062a\u062e\u062f\u0645 \u0641\u064a \u0627\u0644\u062a\u0635\u0645\u064a\u0645 \u0627\u0644\u0647\u0646\u062f\u0633\u064a\u060c \u0648\u0627\u0644\u0631\u0633\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629\u060c \u0648\u0627\u0644\u0646\u0645\u0630\u062c\u0629 \u062b\u0644\u0627\u062b\u064a\u0629 \u0627\u0644\u0623\u0628\u0639\u0627\u062f\u060c \u0648\u0623\u0646\u0638\u0645\u0629 \u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0627\u0644\u062c\u063a\u0631\u0627\u0641\u064a\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u064a \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a<\/h2>\n<p>\u062a\u0647\u062f\u0641 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0625\u0644\u0649 \u0625\u064a\u062c\u0627\u062f \u0642\u064a\u0645\u0629 \u0639\u0638\u0645\u0649 \u0623\u0648 \u0635\u063a\u0631\u0649 \u0644\u062f\u0627\u0644\u0629\u060c \u0645\u0639 \u0623\u0648 \u062f\u0648\u0646 \u0642\u064a\u0648\u062f. \u0648\u062a\u0648\u062c\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0639\u062f\u064a\u062f\u0629 \u0644\u0645\u0639\u0627\u0644\u062c\u0629 \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0626\u0644\u060c \u0645\u0646\u0647\u0627 \u0637\u0631\u0642 \u062a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a\u060c \u0648\u0637\u0631\u0642 \u062a\u0643\u0631\u0627\u0631\u064a\u0629\u060c \u0648\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0628\u0631\u0645\u062c\u0629 \u0627\u0644\u062e\u0637\u064a\u0629\u060c \u0648\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0627\u0644\u0645\u062d\u062f\u0628.<\/p>\n<p>\u062a\u0638\u0647\u0631 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0641\u064a \u0627\u0644\u0627\u0642\u062a\u0635\u0627\u062f \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0644\u062a\u062e\u0637\u064a\u0637 \u0648\u0627\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a. \u0648\u062a\u062e\u062a\u0644\u0641 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0645\u0646\u0627\u0633\u0628\u0629 \u0628\u062d\u0633\u0628 \u0628\u0646\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629\u060c \u0648\u0648\u062c\u0648\u062f \u0627\u0644\u0642\u064a\u0648\u062f\u060c \u0648\u062d\u062c\u0645 \u0627\u0644\u0645\u0633\u0623\u0644\u0629\u060c \u0648\u0645\u062f\u0649 \u062a\u0648\u0641\u0631 \u0645\u0639\u0644\u0648\u0645\u0627\u062a \u0639\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0631\u0633\u0648\u0645<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u062a\u0645\u062b\u064a\u0644 \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0628\u0634\u0628\u0643\u0627\u062a \u062a\u062a\u0643\u0648\u0646 \u0645\u0646 \u0631\u0624\u0648\u0633 \u0648\u062d\u0648\u0627\u0641\u060c \u0648\u062a\u0633\u0645\u0649 \u0627\u0644\u0631\u0633\u0648\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u064a\u0629. \u0648\u062a\u0633\u062a\u062e\u062f\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u062e\u0627\u0635\u0629 \u0644\u0644\u0628\u062d\u062b \u0639\u0646 \u0627\u0644\u0645\u0633\u0627\u0631\u0627\u062a\u060c \u0648\u0625\u064a\u062c\u0627\u062f \u0623\u0642\u0635\u0631 \u0637\u0631\u064a\u0642\u060c \u0648\u0627\u0643\u062a\u0634\u0627\u0641 \u0627\u0644\u0645\u0643\u0648\u0646\u0627\u062a\u060c \u0648\u0628\u0646\u0627\u0621 \u0627\u0644\u0623\u0634\u062c\u0627\u0631 \u0627\u0644\u0645\u0645\u062a\u062f\u0629\u060c \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u0646\u064a\u0629 \u0627\u0644\u0634\u0628\u0643\u064a\u0629.<\/p>\n<p>\u0648\u0631\u063a\u0645 \u0623\u0646 \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0631\u0633\u0648\u0645 \u062a\u0637\u0648\u0631\u062a \u0623\u0635\u0644\u0627\u064b \u0628\u0648\u0635\u0641\u0647\u0627 \u0641\u0631\u0639\u0627\u064b \u0631\u064a\u0627\u0636\u064a\u0627\u064b\u060c \u0641\u0625\u0646 \u0637\u0628\u064a\u0639\u0629 \u0645\u0633\u0627\u0626\u0644\u0647\u0627 \u062c\u0639\u0644\u062a\u0647\u0627 \u0645\u062c\u0627\u0644\u0627\u064b \u0645\u0631\u0643\u0632\u064a\u0627\u064b \u0641\u064a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a\u060c \u0644\u0623\u0646\u0647\u0627 \u062a\u0642\u062f\u0645 \u0623\u0645\u062b\u0644\u0629 \u0648\u0627\u0636\u062d\u0629 \u0639\u0644\u0649 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0648\u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062d\u0633\u0627\u0628\u064a.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u0631\u0645\u0632\u064a<\/h2>\n<p>\u0644\u0627 \u062a\u062a\u0639\u0627\u0645\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u062f\u0627\u0626\u0645\u0627\u064b \u0645\u0639 \u0623\u0639\u062f\u0627\u062f \u0645\u062d\u062f\u062f\u0629\u061b \u0641\u0642\u062f \u062a\u0639\u0645\u0644 \u0639\u0644\u0649 \u0631\u0645\u0648\u0632 \u0648\u062a\u0639\u0628\u064a\u0631\u0627\u062a \u062c\u0628\u0631\u064a\u0629. \u0648\u062a\u0634\u0645\u0644 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0631\u0645\u0632\u064a\u0629 \u062a\u0628\u0633\u064a\u0637 \u0627\u0644\u062a\u0639\u0628\u064a\u0631\u0627\u062a\u060c \u0648\u0627\u0644\u062a\u0641\u0627\u0636\u0644 \u0627\u0644\u0631\u0645\u0632\u064a\u060c \u0648\u0627\u0644\u062a\u0643\u0627\u0645\u0644 \u0641\u064a \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0627\u0644\u0645\u0645\u0643\u0646\u0629\u060c \u0648\u062a\u062d\u0644\u064a\u0644 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f\u060c \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631 \u0644\u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f.<\/p>\n<p>\u064a\u0645\u0643\u0646 \u062a\u0637\u0628\u064a\u0642 \u0627\u0644\u0646\u0633\u062e\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0645\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631 \u0639\u0644\u0649 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0623\u064a\u0636\u0627\u064b\u060c \u062d\u064a\u062b \u062a\u062a\u0646\u0627\u0642\u0635 \u062f\u0631\u062c\u0627\u062a \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0628\u0642\u064a\u0629 \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u062a\u0646\u0627\u0642\u0635 \u0627\u0644\u0642\u064a\u0645 \u0627\u0644\u0639\u062f\u062f\u064a\u0629. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Euclidean_algorithm\" title=\"17|Euclidean algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[17]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a<\/h2>\n<p>\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a \u064a\u062f\u0631\u0633 \u0627\u0644\u0628\u0648\u0627\u0642\u064a \u0639\u0646\u062f \u0627\u0644\u0642\u0633\u0645\u0629 \u0639\u0644\u0649 \u0639\u062f\u062f \u0645\u0639\u064a\u0646\u060c \u0648\u062a\u0638\u0647\u0631 \u0641\u064a\u0647 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0644\u0625\u062c\u0631\u0627\u0621 \u0639\u0645\u0644\u064a\u0627\u062a \u0645\u062b\u0644 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u0639\u0643\u0648\u0633\u0627\u062a \u0648\u062d\u0644 \u0628\u0639\u0636 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a\u0629. \u0648\u062a\u0644\u0639\u0628 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0625\u0642\u0644\u064a\u062f\u064a\u0629 \u0627\u0644\u0645\u0648\u0633\u0639\u0629 \u062f\u0648\u0631\u0627\u064b \u0645\u0647\u0645\u0627\u064b \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0644\u0623\u0646\u0647\u0627 \u062a\u0633\u062a\u0637\u064a\u0639 \u0625\u064a\u062c\u0627\u062f \u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0628\u0632\u0648 \u0627\u0644\u0644\u0627\u0632\u0645\u0629 \u0644\u0628\u0646\u0627\u0621 \u0627\u0644\u0645\u0639\u0643\u0648\u0633 \u0627\u0644\u0636\u0631\u0628\u064a \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0645\u0648\u062c\u0648\u062f\u0627\u064b.<\/p>\n<p>\u0648\u0642\u062f \u0623\u062f\u0649 \u0627\u0644\u062a\u0637\u0648\u0631 \u0627\u0644\u0643\u0628\u064a\u0631 \u0641\u064a \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0625\u0644\u0649 \u062c\u0639\u0644 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0639\u0645\u0644\u064a\u0629 \u0641\u064a \u0645\u062c\u0627\u0644\u0627\u062a \u062a\u0637\u0628\u064a\u0642\u064a\u0629 \u0639\u062f\u064a\u062f\u0629\u060c \u0645\u0639 \u0628\u0642\u0627\u0621 \u0627\u0644\u0623\u0633\u0626\u0644\u0629 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0643\u0641\u0627\u0621\u0629 \u0628\u0639\u0636 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0645\u0646 \u0645\u0648\u0636\u0648\u0639\u0627\u062a \u0627\u0644\u0628\u062d\u062b \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0645\u0633\u062a\u0645\u0631.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062d\u0633\u0627\u0628<\/h2>\n<p>\u0623\u062f\u0649 \u0627\u0644\u0633\u0624\u0627\u0644 \u0639\u0646 \u0645\u0639\u0646\u0649 \u00ab\u0625\u062c\u0631\u0627\u0621 \u062d\u0633\u0627\u0628\u064a\u00bb \u0625\u0644\u0649 \u062a\u0637\u0648\u0631 \u0623\u062d\u062f \u0623\u0647\u0645 \u0645\u0648\u0636\u0648\u0639\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629: \u0645\u0627 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628\u0647 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u064b\u061f \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u0639\u0634\u0631\u064a\u0646 \u0638\u0647\u0631\u062a \u0646\u0645\u0627\u0630\u062c \u0631\u064a\u0627\u0636\u064a\u0629 \u0631\u0633\u0645\u064a\u0629 \u0644\u0644\u062d\u0633\u0627\u0628\u060c \u0645\u0646 \u0628\u064a\u0646\u0647\u0627 \u0622\u0644\u0629 \u062a\u0648\u0631\u0646\u063a \u0648\u062d\u0633\u0627\u0628 \u0644\u0627\u0645\u0628\u062f\u0627 \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0639\u0648\u062f\u064a\u0629 \u0627\u0644\u0639\u0627\u0645\u0629.<\/p>\n<p>\u0648\u0642\u062f \u0623\u0638\u0647\u0631\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062d\u0633\u0627\u0628 \u0623\u0646 \u0648\u062c\u0648\u062f \u0648\u0635\u0641 \u0631\u064a\u0627\u0636\u064a \u0644\u0644\u0645\u0633\u0623\u0644\u0629 \u0644\u0627 \u064a\u0639\u0646\u064a \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u0648\u062c\u0648\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u0627\u0645\u0629 \u062a\u062d\u0644\u0647\u0627. \u0648\u0645\u0646 \u0623\u0647\u0645 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0641\u064a \u0647\u0630\u0627 \u0627\u0644\u0633\u064a\u0627\u0642 \u0639\u062f\u0645 \u0642\u0627\u0628\u0644\u064a\u0629 \u0628\u0639\u0636 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0644\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a \u0627\u0644\u0639\u0627\u0645\u060c \u0648\u0647\u0648 \u0645\u0627 \u0623\u0639\u0627\u062f \u062a\u0639\u0631\u064a\u0641 \u062d\u062f\u0648\u062f \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062d\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0641\u064a \u0627\u0644\u0639\u0635\u0631 \u0627\u0644\u062d\u062f\u064a\u062b. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Algorithm\" title=\"18|Algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[18]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646<\/h2>\n<p>\u062a\u0648\u062c\u062f \u0639\u0644\u0627\u0642\u0629 \u0639\u0645\u064a\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0648\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629. \u0641\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0642\u062f \u064a\u062b\u0628\u062a \u0648\u062c\u0648\u062f \u0643\u0627\u0626\u0646 \u0631\u064a\u0627\u0636\u064a \u062f\u0648\u0646 \u0623\u0646 \u064a\u0639\u0637\u064a \u0637\u0631\u064a\u0642\u0629 \u0639\u0645\u0644\u064a\u0629 \u0644\u0628\u0646\u0627\u0626\u0647\u060c \u0628\u064a\u0646\u0645\u0627 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0642\u062f\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0637\u0631\u064a\u0642\u0629 \u0635\u0631\u064a\u062d\u0629 \u0644\u0628\u0646\u0627\u0621 \u0630\u0644\u0643 \u0627\u0644\u0643\u0627\u0626\u0646. \u0648\u0641\u064a \u0628\u0639\u0636 \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u0623\u0635\u0628\u062d\u062a \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0625\u062b\u0628\u0627\u062a \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0623\u0643\u062b\u0631 \u0645\u0628\u0627\u0634\u0631\u0629\u060c \u0643\u0645\u0627 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u0648\u0627\u0644\u0645\u0646\u0637\u0642 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a.<\/p>\n<p>\u0648\u062a\u062a\u064a\u062d \u0628\u0639\u0636 \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u062e\u0637\u0648\u0627\u062a \u0628\u0646\u0627\u0621 \u0645\u0646\u0637\u0642\u064a\u0629\u060c \u0628\u064a\u0646\u0645\u0627 \u0642\u062f \u062a\u0643\u0648\u0646 \u0647\u0646\u0627\u0643 \u0628\u0631\u0627\u0647\u064a\u0646 \u0648\u062c\u0648\u062f\u064a\u0629 \u0644\u0627 \u062a\u0642\u062f\u0645 \u0628\u0627\u0644\u0636\u0631\u0648\u0631\u0629 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u0645\u0644\u064a\u0629 \u0630\u0627\u062a \u0643\u0641\u0627\u0621\u0629 \u0645\u0639\u0642\u0648\u0644\u0629. \u0644\u0630\u0644\u0643 \u0641\u0625\u0646 \u00ab\u0625\u062b\u0628\u0627\u062a \u0627\u0644\u0648\u062c\u0648\u062f\u00bb \u0648\u00ab\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0634\u064a\u0621 \u0641\u0639\u0644\u064a\u0627\u064b\u00bb \u0644\u064a\u0633\u0627 \u062f\u0627\u0626\u0645\u0627\u064b \u0627\u0644\u0623\u0645\u0631 \u0646\u0641\u0633\u0647.<\/p>\n<h2>\u0627\u0644\u0643\u0641\u0627\u0621\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0646 \u0639\u062f\u0629 \u0632\u0648\u0627\u064a\u0627: \u0635\u062d\u0629 \u0627\u0644\u0646\u062a\u064a\u062c\u0629\u060c \u0648\u0636\u0648\u062d \u0627\u0644\u062e\u0637\u0648\u0627\u062a\u060c \u0636\u0645\u0627\u0646 \u0627\u0644\u062a\u0648\u0642\u0641\u060c \u0639\u062f\u062f \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a\u060c \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0630\u0627\u0643\u0631\u0629\u060c \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0627\u0644\u0639\u062f\u062f\u064a\u060c \u0648\u062f\u0642\u0629 \u0627\u0644\u0646\u062a\u064a\u062c\u0629. \u0648\u0642\u062f \u062a\u0643\u0648\u0646 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0627 \u0635\u062d\u064a\u062d\u0629 \u062a\u0645\u0627\u0645\u0627\u064b \u0644\u0643\u0646\u0647\u0627 \u063a\u064a\u0631 \u0639\u0645\u0644\u064a\u0629 \u0628\u0633\u0628\u0628 \u0627\u0631\u062a\u0641\u0627\u0639 \u062a\u0643\u0644\u0641\u0629 \u0627\u0644\u062d\u0633\u0627\u0628.<\/p>\n<p>\u0644\u0647\u0630\u0627 \u0623\u0635\u0628\u062d\u062a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062a\u0639\u0642\u064a\u062f \u062c\u0632\u0621\u0627\u064b \u0623\u0633\u0627\u0633\u064a\u0627\u064b \u0645\u0646 \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a. \u0641\u0627\u0644\u0633\u0624\u0627\u0644 \u0644\u0645 \u064a\u0639\u062f \u0641\u0642\u0637 \u00ab\u0647\u0644 \u062a\u0648\u062c\u062f \u0637\u0631\u064a\u0642\u0629 \u0644\u0644\u062d\u0644\u061f\u00bb\u060c \u0628\u0644 \u0623\u0635\u0628\u062d \u0623\u064a\u0636\u0627\u064b \u00ab\u0645\u0627 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062a\u064a \u062a\u062d\u062a\u0627\u062c\u0647\u0627 \u0647\u0630\u0647 \u0627\u0644\u0637\u0631\u064a\u0642\u0629\u061f \u0648\u0647\u0644 \u062a\u0648\u062c\u062f \u0637\u0631\u064a\u0642\u0629 \u0623\u0633\u0631\u0639\u061f\u00bb.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f<\/h2>\n<p>\u062a\u0639\u062f \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u064a \u064a\u0643\u0648\u0646 \u0632\u0645\u0646 \u062a\u0646\u0641\u064a\u0630\u0647\u0627 \u0645\u062d\u062f\u0648\u062f\u0627\u064b \u0628\u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f \u0641\u064a \u062d\u062c\u0645 \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0641\u0626\u0629 \u0645\u0647\u0645\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062a\u0639\u0642\u064a\u062f. \u0648\u064a\u0634\u0627\u0631 \u0639\u0627\u062f\u0629 \u0625\u0644\u0649 \u0647\u0630\u0647 \u0627\u0644\u0641\u0626\u0629 \u0628\u0627\u0644\u0631\u0645\u0632 <i>P<\/i>. \u0648\u062a\u0639\u062f \u062f\u0631\u0627\u0633\u0629 \u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062d\u0644 \u0628\u0643\u0641\u0627\u0621\u0629 \u0648\u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u064a \u062a\u0628\u062f\u0648 \u0623\u0635\u0639\u0628 \u0645\u0646 \u0630\u0644\u0643 \u0645\u0646 \u0623\u0639\u0642\u062f \u0645\u0648\u0636\u0648\u0639\u0627\u062a \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0627\u0644\u0646\u0638\u0631\u064a\u0629.<\/p>\n<p>\u0648\u0644\u0627 \u064a\u0646\u0628\u063a\u064a \u0645\u0633\u0627\u0648\u0627\u0629 \u00ab\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629\u00bb \u0628\u0640\u00ab\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u062d\u062f\u0648\u062f\u00bb\u061b \u0641\u0627\u0644\u0623\u0648\u0644\u0649 \u0648\u0635\u0641 \u0639\u0627\u0645 \u0644\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629\u060c \u0628\u064a\u0646\u0645\u0627 \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u062a\u0635\u0646\u064a\u0641 \u064a\u0639\u062a\u0645\u062f \u0639\u0644\u0649 \u0646\u0645\u0648 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u064a\u0629<\/h2>\n<p>\u0641\u064a \u0628\u0639\u0636 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0644\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0627\u0644\u062d\u0644 \u0627\u0644\u0623\u0645\u062b\u0644 \u0623\u0648 \u0627\u0644\u062f\u0642\u064a\u0642 \u0639\u0645\u0644\u064a\u0627\u064b. \u0639\u0646\u062f\u0626\u0630 \u062a\u0633\u062a\u062e\u062f\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u062a\u0642\u0631\u064a\u0628\u064a\u0629 \u062a\u0647\u062f\u0641 \u0625\u0644\u0649 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u062d\u0644 \u0642\u0631\u064a\u0628 \u0645\u0646 \u0627\u0644\u0647\u062f\u0641 \u0636\u0645\u0646 \u0636\u0645\u0627\u0646\u0627\u062a \u0623\u0648 \u062d\u062f\u0648\u062f \u0645\u0639\u064a\u0646\u0629.<\/p>\n<p>\u062a\u0638\u0647\u0631 \u0647\u0630\u0647 \u0627\u0644\u0641\u0643\u0631\u0629 \u062e\u0635\u0648\u0635\u0627\u064b \u0641\u064a \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0648\u0627\u0644\u0645\u0639\u0642\u062f\u0629\u060c \u062d\u064a\u062b \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0643\u0648\u0646 \u062a\u0643\u0644\u0641\u0629 \u0627\u0644\u062d\u0644 \u0627\u0644\u062f\u0642\u064a\u0642 \u0645\u0631\u062a\u0641\u0639\u0629 \u062c\u062f\u0627\u064b. \u0648\u064a\u0635\u0628\u062d \u0627\u0644\u0633\u0624\u0627\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0639\u0646\u062f\u0626\u0630 \u0645\u062a\u0639\u0644\u0642\u0627\u064b \u0628\u0645\u062f\u0649 \u062c\u0648\u062f\u0629 \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u060c \u0648\u0628\u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0639\u0644\u0649 \u0644\u0644\u062e\u0637\u0623\u060c \u0648\u0628\u0633\u0631\u0639\u0629 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0627\u0644\u062d\u0644.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0648\u0645\u062d\u0627\u0643\u0627\u0629 \u0645\u0648\u0646\u062a \u0643\u0627\u0631\u0644\u0648<\/h2>\n<p>\u062a\u0633\u062a\u062e\u062f\u0645 \u0645\u062d\u0627\u0643\u0627\u0629 \u0645\u0648\u0646\u062a \u0643\u0627\u0631\u0644\u0648 \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0623\u0648 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0639\u0634\u0648\u0627\u0626\u064a\u0629 \u0644\u062a\u0642\u062f\u064a\u0631 \u0643\u0645\u064a\u0627\u062a \u0631\u064a\u0627\u0636\u064a\u0629\u060c \u062e\u0635\u0648\u0635\u0627\u064b \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0628\u0627\u0634\u0631 \u0635\u0639\u0628\u0627\u064b. \u0648\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647\u0627 \u0644\u062a\u0642\u0631\u064a\u0628 \u062a\u0643\u0627\u0645\u0644\u0627\u062a \u0623\u0648 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u062a \u0623\u0648 \u062e\u0635\u0627\u0626\u0635 \u0644\u0646\u0638\u0645 \u0645\u0639\u0642\u062f\u0629.<\/p>\n<p>\u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0644\u0627 \u062a\u0643\u0648\u0646 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0639\u0627\u062f\u0629 \u062b\u0627\u0628\u062a\u0629 \u062a\u0645\u0627\u0645\u0627\u064b \u0645\u0646 \u062a\u0634\u063a\u064a\u0644 \u0625\u0644\u0649 \u0622\u062e\u0631\u060c \u0628\u0644 \u062a\u0631\u062a\u0628\u0637 \u0628\u062f\u0642\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u064a\u0645\u0643\u0646 \u062a\u062d\u0633\u064a\u0646\u0647\u0627 \u0628\u0632\u064a\u0627\u062f\u0629 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629. \u0648\u064a\u0635\u0628\u062d \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a \u062c\u0632\u0621\u0627\u064b \u0645\u0646 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0646\u0641\u0633\u0647\u0627.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0627\u0632\u064a\u0629<\/h2>\n<p>\u0645\u0639 \u062a\u0637\u0648\u0631 \u0627\u0644\u062d\u0648\u0627\u0633\u064a\u0628 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u0645\u0639\u0627\u0644\u062c\u0627\u062a\u060c \u0623\u0635\u0628\u062d \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u062a\u0635\u0645\u064a\u0645 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u064a\u0645\u0643\u0646 \u062a\u0642\u0633\u064a\u0645 \u0639\u0645\u0644\u064a\u0627\u062a\u0647\u0627 \u0625\u0644\u0649 \u0623\u062c\u0632\u0627\u0621 \u062a\u0646\u0641\u0630 \u0628\u0627\u0644\u062a\u0648\u0627\u0632\u064a. \u0648\u062a\u0638\u0647\u0631 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u062c\u0629 \u0641\u064a \u0636\u0631\u0628 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a\u060c \u0648\u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629\u060c \u0648\u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0625\u0634\u0627\u0631\u0627\u062a\u060c \u0648\u062d\u0644 \u0628\u0639\u0636 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/p>\n<p>\u0644\u0643\u0646 \u0644\u064a\u0633\u062a \u0643\u0644 \u0645\u0633\u0623\u0644\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u0648\u0627\u0632\u064a \u0628\u0635\u0648\u0631\u0629 \u0641\u0639\u0627\u0644\u0629\u061b \u0641\u0648\u062c\u0648\u062f \u0627\u0639\u062a\u0645\u0627\u062f \u0645\u062a\u0633\u0644\u0633\u0644 \u0628\u064a\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0642\u062f \u064a\u062d\u062f \u0645\u0646 \u0645\u0642\u062f\u0627\u0631 \u0627\u0644\u0639\u0645\u0644 \u0627\u0644\u0630\u064a \u064a\u0645\u0643\u0646 \u062a\u0646\u0641\u064a\u0630\u0647 \u0641\u064a \u0627\u0644\u0648\u0642\u062a \u0646\u0641\u0633\u0647. \u0648\u0644\u0630\u0644\u0643 \u0623\u0635\u0628\u062d\u062a \u0642\u0627\u0628\u0644\u064a\u0629 \u0627\u0644\u062a\u0648\u0627\u0632\u064a \u062e\u0627\u0635\u064a\u0629 \u0645\u0647\u0645\u0629 \u0639\u0646\u062f \u062a\u0635\u0645\u064a\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0648\u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629<\/h2>\n<p>\u0623\u062f\u062a \u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629 \u0625\u0644\u0649 \u062a\u062d\u0648\u0644 \u0643\u0628\u064a\u0631 \u0641\u064a \u062f\u0648\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629. \u0641\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u064a \u0643\u0627\u0646 \u062d\u0644\u0647\u0627 \u064a\u062a\u0637\u0644\u0628 \u062d\u0633\u0627\u0628\u0627\u062a \u064a\u062f\u0648\u064a\u0629 \u0637\u0648\u064a\u0644\u0629 \u064a\u0645\u0643\u0646 \u0627\u0644\u064a\u0648\u0645 \u062a\u062d\u0648\u064a\u0644\u0647\u0627 \u0625\u0644\u0649 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u062a\u0646\u0641\u0630 \u0645\u0644\u0627\u064a\u064a\u0646 \u0623\u0648 \u0645\u0644\u064a\u0627\u0631\u0627\u062a \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a. \u0644\u0643\u0646 \u0632\u064a\u0627\u062f\u0629 \u0627\u0644\u0642\u062f\u0631\u0629 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u0644\u0627 \u062a\u0644\u063a\u064a \u0627\u0644\u062d\u0627\u062c\u0629 \u0625\u0644\u0649 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u061b \u0628\u0644 \u062a\u062c\u0639\u0644 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631 \u0648\u0627\u0644\u062e\u0637\u0623 \u0648\u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0623\u0643\u062b\u0631 \u0623\u0647\u0645\u064a\u0629.<\/p>\n<p>\u0648\u0642\u062f \u0623\u0634\u0627\u0631\u062a \u0627\u0644\u0623\u062f\u0628\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0625\u0644\u0649 \u0623\u0646 \u062a\u0637\u0648\u0631 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u062c\u062f\u064a\u062f\u0629\u060c \u0645\u062b\u0644 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a <i>QR<\/i> \u0648FFT \u0648\u0637\u0631\u0642 \u0627\u0644\u0634\u0628\u0643\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u0645\u0633\u062a\u0648\u064a\u0627\u062a \u0648\u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u0637\u064a\u0641\u064a\u0629\u060c \u0643\u0627\u0646 \u0644\u0647 \u0623\u062b\u0631 \u0643\u0628\u064a\u0631 \u0641\u064a \u062a\u0637\u0648\u0631 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0639\u0644\u0645\u064a. <sup class=\"ref\"><a href=\"https:\/\/www.ams.org\/bull\/2012-49-04\/S0273-0979-2012-01379-4\/S0273-0979-2012-01379-4.pdf\" title=\"19|Numerical algorithms and the development of computational mathematics|Eitan Tadmor, Bulletin of the American Mathematical Society|2012\" target=\"_blank\" rel=\"noopener\">[19]<\/a><\/sup><\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0648\u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a<\/h2>\n<p>\u062a\u0639\u062a\u0645\u062f \u0643\u062b\u064a\u0631 \u0645\u0646 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0630\u0643\u0627\u0621 \u0627\u0644\u0627\u0635\u0637\u0646\u0627\u0639\u064a \u0648\u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u064a \u0639\u0644\u0649 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0631\u064a\u0627\u0636\u064a\u0629 \u0644\u0644\u062a\u062f\u0631\u064a\u0628 \u0648\u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u0627\u062a \u0648\u0645\u0639\u0627\u0644\u062c\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a. \u0648\u062a\u0638\u0647\u0631 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0627\u0646\u062d\u062f\u0627\u0631 \u0648\u0627\u0644\u062a\u062d\u062f\u064a\u062b \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u064a \u0648\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0648\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0641\u064a \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u062a\u0639\u0644\u0645 \u0627\u0644\u0622\u0644\u064a.<\/p>\n<p>\u0648\u0647\u0646\u0627 \u062a\u0638\u0647\u0631 \u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0628\u0648\u0636\u0648\u062d: \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u0642\u062f \u064a\u0643\u0648\u0646 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u062f\u0627\u0644\u0629 \u0630\u0627\u062a \u0639\u062f\u062f \u0643\u0628\u064a\u0631 \u0645\u0646 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a\u060c \u0648\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0647\u064a \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0643\u064a\u0641 \u062a\u062a\u063a\u064a\u0631 \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0627\u0645\u0644\u0627\u062a \u0628\u0647\u062f\u0641 \u062a\u0642\u0644\u064a\u0644 \u062f\u0627\u0644\u0629 \u062e\u0633\u0627\u0631\u0629 \u0623\u0648 \u062a\u062d\u0633\u064a\u0646 \u0645\u0639\u064a\u0627\u0631 \u0645\u0639\u064a\u0646.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u062d\u0627\u0633\u0648\u0628<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u062d\u0627\u0644\u0627\u062a \u0643\u062b\u064a\u0631\u0629 \u0645\u0646 \u0645\u0633\u0623\u0644\u0629 \u0631\u064a\u0627\u0636\u064a\u0629\u060c \u0623\u0648 \u0644\u0625\u062c\u0631\u0627\u0621 \u062d\u0633\u0627\u0628\u0627\u062a \u0636\u062e\u0645\u0629 \u062a\u0633\u0627\u0639\u062f \u0627\u0644\u0628\u0627\u062d\u062b \u0641\u064a \u0627\u0643\u062a\u0634\u0627\u0641 \u0646\u0645\u0637 \u0623\u0648 \u0627\u062e\u062a\u0628\u0627\u0631 \u062a\u062e\u0645\u064a\u0646. \u0644\u0643\u0646 \u0627\u0644\u062a\u062d\u0642\u0642 \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u0645\u0646 \u0639\u062f\u062f \u0643\u0628\u064a\u0631 \u0645\u0646 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0644\u0627 \u064a\u0639\u0627\u062f\u0644 \u062f\u0627\u0626\u0645\u0627\u064b \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0639\u0627\u0645\u060c \u0625\u0644\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062d\u0633\u0627\u0628\u064a \u062c\u0632\u0621\u0627\u064b \u0645\u0646 \u0628\u0631\u0647\u0627\u0646 \u0645\u0648\u062b\u0642 \u0623\u0648 \u0643\u0627\u0646 \u0641\u0636\u0627\u0621 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0645\u062d\u062f\u0648\u062f\u0627\u064b \u0628\u0635\u0648\u0631\u0629 \u062a\u062c\u0639\u0644 \u0627\u0644\u0641\u062d\u0635 \u0634\u0627\u0645\u0644\u0627\u064b.<\/p>\n<p>\u0648\u0642\u062f \u0623\u062f\u0649 \u0630\u0644\u0643 \u0625\u0644\u0649 \u0638\u0647\u0648\u0631 \u0645\u062c\u0627\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u0627\u0644\u0630\u064a \u064a\u062c\u0645\u0639 \u0628\u064a\u0646 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0631\u0645\u0632\u064a \u0648\u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0639\u0627\u0644\u064a\u0629 \u0627\u0644\u0623\u062f\u0627\u0621.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a<\/h2>\n<p>\u0627\u0644\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0637\u0648\u064a\u0644 \u0644\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u064a\u0648\u0636\u062d \u0623\u0646 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a \u0644\u064a\u0633 \u0646\u062a\u0627\u062c \u0627\u0644\u0639\u0635\u0631 \u0627\u0644\u0631\u0642\u0645\u064a. \u0641\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u062a\u0631\u062c\u0639 \u0625\u0644\u0649 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u064a\u0648\u0646\u0627\u0646\u064a\u0629 \u0627\u0644\u0642\u062f\u064a\u0645\u0629\u060c \u0648\u0637\u0631\u0642 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0639\u062f\u062f\u064a \u0648\u0627\u0644\u062c\u062f\u0627\u0648\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u062a\u0637\u0648\u0631\u062a \u0639\u0628\u0631 \u0627\u0644\u062d\u0636\u0627\u0631\u0627\u062a \u0627\u0644\u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0628\u064a\u0646\u0645\u0627 \u0627\u0643\u062a\u0633\u0628 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b \u0627\u0633\u0645\u0647 \u0645\u0646 \u0627\u0644\u0644\u0627\u062a\u064a\u0646\u064a\u0629 \u0627\u0644\u0648\u0633\u064a\u0637\u0629 \u0627\u0644\u0645\u0631\u062a\u0628\u0637\u0629 \u0628\u0627\u0633\u0645 \u0627\u0644\u0639\u0627\u0644\u0645 \u0645\u062d\u0645\u062f \u0628\u0646 \u0645\u0648\u0633\u0649 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u060c \u0627\u0644\u0630\u064a \u0627\u0631\u062a\u0628\u0637\u062a \u0623\u0639\u0645\u0627\u0644\u0647 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0628\u062a\u0627\u0631\u064a\u062e \u0627\u0646\u062a\u0642\u0627\u0644 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0625\u0644\u0649 \u0623\u0648\u0631\u0648\u0628\u0627.<\/p>\n<p>\u0648\u0642\u062f \u0623\u0635\u0628\u062d \u0627\u0644\u0627\u0633\u0645 \u00abalgorithm\u00bb \u0641\u064a \u0627\u0644\u0644\u063a\u0627\u062a \u0627\u0644\u0623\u0648\u0631\u0648\u0628\u064a\u0629 \u0645\u0631\u062a\u0628\u0637\u0627\u064b \u062a\u0627\u0631\u064a\u062e\u064a\u0627\u064b \u0628\u0627\u0633\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u060c \u062b\u0645 \u0627\u062a\u0633\u0639 \u0645\u0639\u0646\u0627\u0647 \u0644\u064a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0627\u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u0645\u0646\u0638\u0645 \u0644\u0644\u062d\u0633\u0627\u0628 \u0628\u0635\u0648\u0631\u0629 \u0639\u0627\u0645\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a \u0648\u062a\u0631\u0627\u062b \u0627\u0644\u062d\u0633\u0627\u0628<\/h2>\n<p>\u0643\u0627\u0646 \u0645\u062d\u0645\u062f \u0628\u0646 \u0645\u0648\u0633\u0649 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a \u0645\u0646 \u0623\u0628\u0631\u0632 \u0639\u0644\u0645\u0627\u0621 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0641\u064a \u0627\u0644\u0639\u0635\u0631 \u0627\u0644\u0639\u0628\u0627\u0633\u064a\u060c \u0648\u0627\u0631\u062a\u0628\u0637 \u0627\u0633\u0645\u0647 \u0628\u0623\u0639\u0645\u0627\u0644 \u0645\u0624\u062b\u0631\u0629 \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u0627\u0644\u062c\u0628\u0631. \u0648\u0642\u062f \u0643\u0627\u0646 \u0627\u0646\u062a\u0642\u0627\u0644 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0627\u0644\u062d\u0633\u0627\u0628\u064a\u0629 \u0627\u0644\u062a\u064a \u0627\u0631\u062a\u0628\u0637\u062a \u0628\u0623\u0639\u0645\u0627\u0644\u0647 \u062c\u0632\u0621\u0627\u064b \u0645\u0646 \u0627\u0644\u062a\u0627\u0631\u064a\u062e \u0627\u0644\u0637\u0648\u064a\u0644 \u0627\u0644\u0630\u064a \u0623\u062f\u0649 \u0625\u0644\u0649 \u0627\u0646\u062a\u0634\u0627\u0631 \u0637\u0631\u0642 \u0627\u0644\u062d\u0633\u0627\u0628 \u0628\u0627\u0644\u0623\u0631\u0642\u0627\u0645 \u0627\u0644\u0647\u0646\u062f\u064a\u0629 \u0627\u0644\u0639\u0631\u0628\u064a\u0629 \u0641\u064a \u0623\u0648\u0631\u0648\u0628\u0627.<\/p>\n<p>\u0648\u0644\u0627 \u064a\u0646\u0628\u063a\u064a \u0627\u0644\u062e\u0644\u0637 \u0628\u064a\u0646 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a \u0628\u0648\u0635\u0641\u0647 \u0639\u0627\u0644\u0645\u0627\u064b \u062a\u0627\u0631\u064a\u062e\u064a\u0627\u064b \u0648\u0628\u064a\u0646 \u00ab\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629\u00bb \u0628\u0648\u0635\u0641\u0647\u0627 \u0645\u0641\u0647\u0648\u0645\u0627\u064b \u062d\u062f\u064a\u062b\u0627\u064b \u0648\u0627\u0633\u0639\u0627\u064b\u061b \u0641\u0627\u0644\u0627\u0633\u0645 \u0627\u0644\u062a\u0627\u0631\u064a\u062e\u064a \u0623\u0633\u0647\u0645 \u0641\u064a \u0646\u0634\u0623\u0629 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u060c \u0628\u064a\u0646\u0645\u0627 \u062a\u0637\u0648\u0631 \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0631\u0633\u0645\u064a \u0644\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0628\u0639\u062f \u0630\u0644\u0643 \u0628\u0642\u0631\u0648\u0646.<\/p>\n<h2>\u0645\u0646 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u064a\u062f\u0648\u064a \u0625\u0644\u0649 \u0627\u0644\u062d\u0627\u0633\u0648\u0628<\/h2>\n<p>\u0642\u0628\u0644 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u060c \u0643\u0627\u0646\u062a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0648\u0633\u064a\u0644\u0629 \u0644\u062a\u0646\u0638\u064a\u0645 \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u064a\u062f\u0648\u064a \u0648\u062a\u0642\u0644\u064a\u0644 \u0627\u0644\u0623\u062e\u0637\u0627\u0621 \u0648\u062a\u0648\u062d\u064a\u062f \u0637\u0631\u0642 \u0627\u0644\u062d\u0644. \u0648\u0645\u0639 \u0638\u0647\u0648\u0631 \u0627\u0644\u0622\u0644\u0627\u062a \u0627\u0644\u062d\u0627\u0633\u0628\u0629 \u0648\u0627\u0644\u062d\u0648\u0627\u0633\u064a\u0628\u060c \u0623\u0635\u0628\u062d\u062a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0648\u0635\u0641\u0627\u064b \u064a\u0645\u0643\u0646 \u062a\u062d\u0648\u064a\u0644\u0647 \u0625\u0644\u0649 \u0628\u0631\u0646\u0627\u0645\u062c \u0648\u062a\u0646\u0641\u064a\u0630\u0647 \u0628\u0633\u0631\u0639\u0629 \u0643\u0628\u064a\u0631\u0629.<\/p>\n<p>\u0644\u0643\u0646 \u0627\u0644\u0645\u0628\u062f\u0623 \u0627\u0644\u0623\u0633\u0627\u0633\u064a \u0644\u0645 \u064a\u062a\u063a\u064a\u0631: \u064a\u062c\u0628 \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0648\u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0648\u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0648\u0634\u0631\u0648\u0637 \u0627\u0644\u062a\u0648\u0642\u0641 \u0648\u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a. \u0627\u0644\u0641\u0631\u0642 \u0647\u0648 \u0623\u0646 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u064a\u0633\u062a\u0637\u064a\u0639 \u062a\u0646\u0641\u064a\u0630 \u0647\u0630\u0647 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0628\u0633\u0631\u0639\u0629 \u0648\u062a\u0643\u0631\u0627\u0631\u0647\u0627 \u0639\u0644\u0649 \u0623\u062d\u062c\u0627\u0645 \u0628\u064a\u0627\u0646\u0627\u062a \u0644\u0627 \u064a\u0633\u062a\u0637\u064a\u0639 \u0627\u0644\u0625\u0646\u0633\u0627\u0646 \u0645\u0639\u0627\u0644\u062c\u062a\u0647\u0627 \u064a\u062f\u0648\u064a\u0627\u064b \u0628\u0643\u0641\u0627\u0621\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0644\u064a\u0633\u062a \u0645\u062c\u0631\u062f \u0648\u0635\u0641 \u0644\u0644\u0628\u0631\u0646\u0627\u0645\u062c<\/h2>\n<p>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0623\u0643\u062b\u0631 \u062a\u062c\u0631\u064a\u062f\u0627\u064b \u0645\u0646 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c. \u064a\u0645\u0643\u0646 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0639\u0646\u0647\u0627 \u0628\u0627\u0644\u0643\u0644\u0645\u0627\u062a \u0623\u0648 \u0627\u0644\u0645\u062e\u0637\u0637 \u0627\u0644\u0627\u0646\u0633\u064a\u0627\u0628\u064a \u0623\u0648 \u0627\u0644\u0635\u064a\u0627\u063a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0623\u0648 \u0634\u0628\u0647 \u0627\u0644\u0628\u0631\u0645\u062c\u064a\u0629. \u0623\u0645\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0641\u064a\u062a\u0637\u0644\u0628 \u0644\u063a\u0629 \u062a\u0646\u0641\u064a\u0630 \u0645\u062d\u062f\u062f\u0629 \u0648\u062a\u0631\u062c\u0645\u0629 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0625\u0644\u0649 \u062a\u0639\u0644\u064a\u0645\u0627\u062a \u064a\u0645\u0643\u0646 \u0644\u0644\u0646\u0638\u0627\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a \u062a\u0646\u0641\u064a\u0630\u0647\u0627.<\/p>\n<p>\u0648\u0644\u0647\u0630\u0627 \u064a\u0645\u0643\u0646 \u0623\u0646 \u062a\u0648\u062c\u062f \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0648\u0627\u062d\u062f\u0629 \u0644\u0647\u0627 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0628\u0644\u063a\u0627\u062a \u0628\u0631\u0645\u062c\u0629 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0623\u0648 \u0639\u0644\u0649 \u0623\u062c\u0647\u0632\u0629 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0623\u0648 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0637\u0631\u0642 \u062a\u0646\u0641\u064a\u0630 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0645\u0639 \u0628\u0642\u0627\u0621 \u0627\u0644\u0641\u0643\u0631\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0646\u0641\u0633\u0647\u0627.<\/p>\n<h2>\u062a\u0635\u0645\u064a\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629<\/h2>\n<p>\u064a\u0628\u062f\u0623 \u062a\u0635\u0645\u064a\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0639\u0627\u062f\u0629 \u0628\u0641\u0647\u0645 \u0628\u0646\u064a\u0629 \u0627\u0644\u0645\u0633\u0623\u0644\u0629. \u062b\u0645 \u062a\u062d\u062f\u062f \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0648\u0627\u0644\u0645\u062e\u0631\u062c\u0627\u062a\u060c \u0648\u062a\u0628\u062d\u062b \u0639\u0646 \u062e\u0627\u0635\u064a\u0629 \u0623\u0648 \u0639\u0644\u0627\u0642\u0629 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u063a\u0644\u0627\u0644\u0647\u0627\u060c \u0648\u0628\u0639\u062f \u0630\u0644\u0643 \u062a\u0635\u0645\u0645 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0648\u062a\u062d\u062f\u062f \u062d\u0627\u0644\u0627\u062a \u0627\u0644\u062a\u0648\u0642\u0641\u060c \u062b\u0645 \u062a\u062b\u0628\u062a \u0627\u0644\u0635\u062d\u0629 \u0648\u062a\u062d\u0644\u0644 \u0627\u0644\u062a\u0639\u0642\u064a\u062f \u0648\u0627\u0644\u062e\u0637\u0623 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u0627\u0644\u062d\u0633\u0627\u0628 \u062a\u0642\u0631\u064a\u0628\u064a\u0627\u064b.<\/p>\n<p>\u0641\u064a \u0627\u0644\u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u060c \u064a\u062c\u0628 \u0625\u0636\u0627\u0641\u0629 \u0633\u0624\u0627\u0644 \u0645\u0647\u0645: \u0647\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0645\u0633\u062a\u0642\u0631\u0629 \u0623\u0645\u0627\u0645 \u0623\u062e\u0637\u0627\u0621 \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u061f \u0641\u0642\u062f \u062a\u0643\u0648\u0646 \u0627\u0644\u0637\u0631\u064a\u0642\u0629 \u0635\u062d\u064a\u062d\u0629 \u0645\u0646 \u0627\u0644\u0646\u0627\u062d\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629\u060c \u0644\u0643\u0646\u0647\u0627 \u062a\u0646\u062a\u062c \u0646\u062a\u0627\u0626\u062c \u0633\u064a\u0626\u0629 \u0639\u0646\u062f \u062a\u0646\u0641\u064a\u0630\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0633\u0627\u0628 \u0645\u062d\u062f\u0648\u062f \u0627\u0644\u062f\u0642\u0629 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0634\u062f\u064a\u062f\u0629 \u0627\u0644\u062d\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u0627\u0636\u0637\u0631\u0627\u0628\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629.<\/p>\n<h2>\u0627\u0644\u0635\u062d\u0629 \u0648\u0627\u0644\u0643\u0641\u0627\u0621\u0629 \u0648\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0627\u0644\u0646\u0638\u0631 \u0625\u0644\u0649 \u062c\u0648\u062f\u0629 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u062b\u0644\u0627\u062b\u0629 \u0645\u062d\u0627\u0648\u0631 \u0645\u062a\u0631\u0627\u0628\u0637\u0629. \u0627\u0644\u0623\u0648\u0644 \u0647\u0648 \u0627\u0644\u0635\u062d\u0629: \u0647\u0644 \u062a\u0639\u0637\u064a \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0645\u0637\u0644\u0648\u0628\u0629\u061f \u0648\u0627\u0644\u062b\u0627\u0646\u064a \u0647\u0648 \u0627\u0644\u0643\u0641\u0627\u0621\u0629: \u0643\u0645 \u062a\u062d\u062a\u0627\u062c \u0645\u0646 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0648\u0627\u0644\u0630\u0627\u0643\u0631\u0629\u061f \u0648\u0627\u0644\u062b\u0627\u0644\u062b \u0647\u0648 \u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631\u060c \u062e\u0635\u0648\u0635\u0627\u064b \u0641\u064a \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0639\u062f\u062f\u064a: \u0647\u0644 \u062a\u0624\u062f\u064a \u0627\u0644\u0623\u062e\u0637\u0627\u0621 \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u0641\u064a \u0627\u0644\u0645\u062f\u062e\u0644\u0627\u062a \u0623\u0648 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0625\u0644\u0649 \u062a\u063a\u064a\u0631\u0627\u062a \u0643\u0628\u064a\u0631\u0629 \u0648\u063a\u064a\u0631 \u0645\u0631\u063a\u0648\u0628\u0629 \u0641\u064a \u0627\u0644\u0646\u0627\u062a\u062c\u061f \u0648\u062a\u0639\u062f \u062f\u0631\u0627\u0633\u0629 \u0647\u0630\u0647 \u0627\u0644\u062c\u0648\u0627\u0646\u0628 \u0627\u0644\u062b\u0644\u0627\u062b\u0629 \u0645\u0646 \u0635\u0645\u064a\u0645 \u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a \u0648\u062a\u0635\u0645\u064a\u0645 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Numerical_analysis\" title=\"20|Numerical analysis|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[20]<\/a><\/sup><\/p>\n<h2>\u0623\u0647\u0645\u064a\u0629 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629<\/h2>\n<p>\u062a\u0645\u0646\u062d \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0642\u062f\u0631\u0629 \u0639\u0645\u0644\u064a\u0629 \u0639\u0644\u0649 \u0627\u0644\u0627\u0646\u062a\u0642\u0627\u0644 \u0645\u0646 \u0627\u0644\u0646\u0638\u0631\u064a\u0629 \u0625\u0644\u0649 \u0627\u0644\u062d\u0633\u0627\u0628. \u0641\u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0645\u0639\u0631\u0641\u0629 \u0623\u0646 \u0627\u0644\u062d\u0644 \u0645\u0648\u062c\u0648\u062f \u0641\u0642\u0637\u060c \u064a\u0645\u0643\u0646 \u0641\u064a \u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0628\u0646\u0627\u0621 \u0637\u0631\u064a\u0642\u0629 \u0644\u0625\u064a\u062c\u0627\u062f\u0647. \u0648\u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0625\u062c\u0631\u0627\u0621 \u062d\u0633\u0627\u0628\u0627\u062a \u0636\u062e\u0645\u0629 \u064a\u062f\u0648\u064a\u0627\u064b\u060c \u064a\u0645\u0643\u0646 \u062a\u062d\u0648\u064a\u0644\u0647\u0627 \u0625\u0644\u0649 \u062e\u0637\u0648\u0627\u062a \u0645\u0646\u0638\u0645\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062a\u0646\u0641\u064a\u0630.<\/p>\n<p>\u0648\u062a\u0638\u0647\u0631 \u0647\u0630\u0647 \u0627\u0644\u0642\u064a\u0645\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f\u060c \u0648\u0627\u0644\u062c\u0628\u0631\u060c \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629\u060c \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u060c \u0648\u0627\u0644\u0625\u062d\u0635\u0627\u0621\u060c \u0648\u0627\u0644\u0641\u064a\u0632\u064a\u0627\u0621\u060c \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629\u060c \u0648\u0627\u0644\u0627\u0642\u062a\u0635\u0627\u062f\u060c \u0648\u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628. \u0643\u0645\u0627 \u0623\u0646 \u062a\u0637\u0648\u0631 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0643\u0627\u0646 \u0623\u062d\u062f \u0627\u0644\u0639\u0648\u0627\u0645\u0644 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u062c\u0639\u0644\u062a \u0627\u0644\u0646\u0645\u0627\u0630\u062c \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u0643\u0628\u064a\u0631\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u062f\u0631\u0627\u0633\u0629 \u0648\u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0628\u0648\u0635\u0641\u0647\u0627 \u062c\u0633\u0631\u0627\u064b \u0628\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628<\/h2>\n<p>\u062a\u0645\u062b\u0644 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0646\u0642\u0637\u0629 \u0627\u0644\u062a\u0642\u0627\u0621 \u0648\u0627\u0636\u062d\u0629 \u0628\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628. \u0641\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u062a\u0648\u0641\u0631 \u0627\u0644\u0628\u0646\u064a\u0629 \u0648\u0627\u0644\u0645\u0646\u0637\u0642 \u0648\u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646\u060c \u0628\u064a\u0646\u0645\u0627 \u062a\u0648\u0641\u0631 \u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628 \u0646\u0645\u0627\u0630\u062c \u0627\u0644\u062a\u0646\u0641\u064a\u0630 \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0648\u0627\u0644\u0644\u063a\u0627\u062a \u0648\u0627\u0644\u0623\u062c\u0647\u0632\u0629.<\/p>\n<p>\u0648\u0642\u062f \u0623\u062f\u0649 \u0647\u0630\u0627 \u0627\u0644\u062a\u062f\u0627\u062e\u0644 \u0625\u0644\u0649 \u0638\u0647\u0648\u0631 \u062a\u062e\u0635\u0635\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629\u060c \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u060c \u0648\u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u0631\u0645\u0632\u064a\u0629\u060c \u0648\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062a\u0639\u0642\u064a\u062f\u060c \u0648\u0627\u0644\u062d\u0648\u0633\u0628\u0629 \u0627\u0644\u0639\u0644\u0645\u064a\u0629. \u0648\u0641\u064a \u062c\u0645\u064a\u0639\u0647\u0627 \u064a\u0628\u0642\u0649 \u0627\u0644\u0633\u0624\u0627\u0644 \u0627\u0644\u0645\u0631\u0643\u0632\u064a \u0642\u0631\u064a\u0628\u0627\u064b \u0645\u0646 \u0627\u0644\u0633\u0624\u0627\u0644 \u0627\u0644\u0631\u064a\u0627\u0636\u064a \u0627\u0644\u0642\u062f\u064a\u0645: \u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u062a\u062d\u0648\u064a\u0644 \u0645\u0633\u0623\u0644\u0629 \u0645\u062c\u0631\u062f\u0629 \u0625\u0644\u0649 \u062e\u0637\u0648\u0627\u062a \u062f\u0642\u064a\u0642\u0629 \u062a\u0642\u0648\u062f \u0625\u0644\u0649 \u0646\u062a\u064a\u062c\u0629 \u0645\u0648\u062b\u0648\u0642\u0629\u061f<\/p>\n<h2>\u0627\u0644\u062e\u0644\u0627\u0635\u0629<\/h2>\n<p>\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0647\u064a \u0625\u062d\u062f\u0649 \u0623\u0647\u0645 \u0635\u0648\u0631 \u0627\u0644\u062a\u0641\u0643\u064a\u0631 \u0627\u0644\u0645\u0646\u0647\u062c\u064a \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a. \u0641\u0647\u064a \u062a\u062d\u0648\u0644 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0645\u0646 \u0635\u064a\u0627\u063a\u0629 \u0646\u0638\u0631\u064a\u0629 \u0625\u0644\u0649 \u0633\u0644\u0633\u0644\u0629 \u0645\u0646 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u0645\u062d\u062f\u062f\u0629 \u0627\u0644\u062a\u064a \u064a\u0645\u0643\u0646 \u062a\u0646\u0641\u064a\u0630\u0647\u0627 \u0648\u062a\u062d\u0644\u064a\u0644\u0647\u0627 \u0648\u0625\u062b\u0628\u0627\u062a \u0635\u062d\u062a\u0647\u0627. \u0648\u0642\u062f \u0628\u062f\u0623\u062a \u0623\u0645\u062b\u0644\u062a\u0647\u0627 \u0627\u0644\u0643\u0628\u0631\u0649 \u0642\u0628\u0644 \u0627\u0644\u0639\u0635\u0631 \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a \u0628\u0648\u0642\u062a \u0637\u0648\u064a\u0644\u060c \u0648\u0645\u0646 \u0623\u0628\u0631\u0632\u0647\u0627 \u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0625\u0642\u0644\u064a\u062f\u0633 \u0627\u0644\u062a\u064a \u0648\u0635\u0641\u0647\u0627 \u0625\u0642\u0644\u064a\u062f\u0633 \u0641\u064a \u00ab\u0627\u0644\u0639\u0646\u0627\u0635\u0631\u00bb \u0644\u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0642\u0627\u0633\u0645 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0627\u0644\u0623\u0643\u0628\u0631\u060c \u062b\u0645 \u062a\u0648\u0633\u0639 \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0639\u0628\u0631 \u0627\u0644\u062c\u0628\u0631 \u0648\u0627\u0644\u062a\u062d\u0644\u064a\u0644 \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0639\u062f\u062f\u064a \u062d\u062a\u0649 \u0623\u0635\u0628\u062d \u062c\u0632\u0621\u0627\u064b \u0645\u0631\u0643\u0632\u064a\u0627\u064b \u0645\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0639\u0644\u0648\u0645 \u0627\u0644\u062d\u0627\u0633\u0648\u0628. <sup class=\"ref\"><a href=\"https:\/\/encyclopediaofmath.org\/wiki\/Euclidean_algorithm\" title=\"21|Euclidean algorithm|Encyclopedia of Mathematics|2020\" target=\"_blank\" rel=\"noopener\">[21]<\/a><\/sup><\/p>\n<p>\u0648\u062a\u062a\u0631\u0627\u0648\u062d \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0627\u0644\u062d\u062f\u064a\u062b\u0629 \u0628\u064a\u0646 \u0627\u0644\u0625\u062c\u0631\u0627\u0621\u0627\u062a \u0627\u0644\u062f\u0642\u064a\u0642\u0629 \u0641\u064a \u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0648\u0627\u0644\u062c\u0628\u0631\u060c \u0648\u0627\u0644\u0637\u0631\u0642 \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u064a\u0629 \u0644\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a\u060c \u0648\u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u0639\u062f\u062f\u064a\u0629 \u0644\u0644\u062a\u0643\u0627\u0645\u0644 \u0648\u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629\u060c \u0648\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0627\u062a \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a\u060c \u0648\u062a\u062d\u0648\u064a\u0644 \u0641\u0648\u0631\u064a\u064a\u0647 \u0627\u0644\u0633\u0631\u064a\u0639\u060c \u0648\u0637\u0631\u0642 \u0627\u0644\u062a\u062d\u0633\u064a\u0646 \u0648\u0627\u0644\u0645\u062d\u0627\u0643\u0627\u0629. \u0648\u0644\u0627 \u062a\u0642\u0627\u0633 \u062c\u0648\u062f\u0629 \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0628\u0635\u062d\u0629 \u0646\u062a\u064a\u062c\u062a\u0647\u0627 \u0641\u0642\u0637\u060c \u0628\u0644 \u0628\u062f\u0642\u0629 \u0627\u0644\u0646\u062a\u064a\u062c\u0629 \u0639\u0646\u062f \u0627\u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0642\u0631\u064a\u0628\u064a\u060c \u0648\u0633\u0631\u0639\u0629 \u0627\u0644\u062a\u0646\u0641\u064a\u0630\u060c \u0648\u0627\u0633\u062a\u0647\u0644\u0627\u0643 \u0627\u0644\u0630\u0627\u0643\u0631\u0629\u060c \u0648\u0627\u0644\u0627\u0633\u062a\u0642\u0631\u0627\u0631\u060c \u0648\u0642\u0627\u0628\u0644\u064a\u062a\u0647\u0627 \u0644\u0644\u062a\u0648\u0633\u0639 \u0645\u0639 \u0627\u0632\u062f\u064a\u0627\u062f \u062d\u062c\u0645 \u0627\u0644\u0645\u0633\u0623\u0644\u0629. \u0648\u0644\u0647\u0630\u0627 \u0623\u0635\u0628\u062d\u062a \u0627\u0644\u062e\u0648\u0627\u0631\u0632\u0645\u064a\u0629 \u0641\u064a \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u062b\u0629 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0645\u062c\u0631\u062f \u00ab\u0637\u0631\u064a\u0642\u0629 \u0644\u0644\u062d\u0633\u0627\u0628\u00bb: \u0625\u0646\u0647\u0627 \u0625\u0637\u0627\u0631 \u064a\u062c\u0645\u0639 \u0628\u064a\u0646 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0648\u0627\u0644\u0628\u0646\u0627\u0621 \u0648\u0627\u0644\u062d\u0633\u0627\u0628 \u0648\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0643\u0641\u0627\u0621\u0629\u060c \u0648\u064a\u0634\u0643\u0644 \u0623\u062d\u062f \u0627\u0644\u0623\u0633\u0633 \u0627\u0644\u062a\u064a \u062a\u0642\u0648\u0645 \u0639\u0644\u064a\u0647\u0627 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0627\u0644\u062d\u0627\u0633\u0648\u0628\u064a\u0629 \u0648\u0627\u0644\u0639\u0644\u0645\u064a\u0629 \u0627\u0644\u0645\u0639\u0627\u0635\u0631\u0629.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0637\u0631\u0642 \u062f\u0642\u064a\u0642\u0629 \u0644\u062d\u0644 \u0627\u0644\u0645\u0633\u0627\u0626\u0644<\/p>\n","protected":false},"author":1,"featured_media":4623,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23],"tags":[],"class_list":["post-4622","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-basic-sciences"],"_links":{"self":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4622","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/comments?post=4622"}],"version-history":[{"count":1,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4622\/revisions"}],"predecessor-version":[{"id":4625,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/posts\/4622\/revisions\/4625"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/media\/4623"}],"wp:attachment":[{"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/media?parent=4622"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/categories?post=4622"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cosmalore.com\/ar\/wp-json\/wp\/v2\/tags?post=4622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}