{"id":365735,"date":"2024-05-21T02:44:22","date_gmt":"2024-05-21T02:44:22","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=365735"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=365735","title":{"rendered":"<span>\u041a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u0432\u0441\u0435 \u043a\u043e\u0440\u043d\u0438 \u0441\u0438\u0441\u0442\u0435\u043c\u044b 2&#215;2?<\/span>"},"content":{"rendered":"<div><!--[--><!--]--><\/div>\n<div id=\"post-content-body\">\n<div>\n<div class=\"article-formatted-body article-formatted-body article-formatted-body_version-2\">\n<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"F_1(x,y) =0,\\;F_2(x,y)=0\" alt=\"F_1(x,y) =0,\\;F_2(x,y)=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/9c8\/ea8\/947\/9c8ea8947686b35804975cc11b4ea73b.svg\" width=\"215\" height=\"22\"\/>, \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0449\u0443\u044e \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e\u043c \u043f\u043e\u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u043d\u043e\u0439 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438: \u0441 \u0440\u043e\u0441\u0442\u043e\u043c <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"x,y\" alt=\"x,y\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f06\/676\/947\/f06676947fc1000c7ec94b3cd70efe02.svg\" width=\"29\" height=\"15\"\/> \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"F_1,F_2\" alt=\"F_1,F_2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/12f\/0ed\/74b\/12f0ed74bf0e7fcd1f5c30f62e0dbfa6.svg\" width=\"51\" height=\"20\"\/> \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0441\u0442\u0443\u0442. \u0417\u0430\u0434\u0430\u0447\u0430 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0438 \u0432\u0441\u0435\u0445 \u043a\u043e\u0440\u043d\u0435\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b.<\/p>\n<h2>\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/h2>\n<p>\u0414\u0432\u0443\u043c\u0435\u0440\u043d\u044b\u0439 \u043c\u0435\u0442\u043e\u0434 \u0431\u0438\u0441\u0435\u043a\u0446\u0438\u0438 \u043e\u0431\u0441\u0443\u0436\u0434\u0430\u043b\u0441\u044f <a href=\"https:\/\/stackoverflow.com\/questions\/3513660\/multivariate-bisection-method\" rel=\"noopener noreferrer nofollow\">\u0437\u0434\u0435\u0441\u044c<\/a>. \u0412\u043e\u043e\u0431\u0449\u0435 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043c\u043d\u043e\u0433\u043e\u043c\u0435\u0440\u043d\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0432\u043e\u0437\u043c\u043e\u0436\u0435\u043d <a href=\"https:\/\/shop.rcd.ru\/catalog\/intervalnyy-analiz-i-ego-prilojeniya\/16552\/\" rel=\"noopener noreferrer nofollow\">\u043c\u0435\u0442\u043e\u0434 \u0432\u0435\u0442\u0432\u0435\u0439 \u0438 \u0433\u0440\u0430\u043d\u0438\u0446<\/a>, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u044e\u0449\u0430\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0440\u0430\u0437\u0431\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u0447\u0430\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0442\u0431\u0440\u0430\u0441\u044b\u0432\u0430\u044e\u0442\u0441\u044f, \u043a\u043e\u0433\u0434\u0430 \u043e\u043d\u0438 \u043d\u0435 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u043c \u043d\u0430\u043b\u0438\u0447\u0438\u044f \u0432 \u043d\u0438\u0445 \u043a\u043e\u0440\u043d\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b. \u0422\u0430\u043a\u0436\u0435 \u0441\u0442\u043e\u0438\u0442 \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0430 \u043f\u043e\u0438\u0441\u043a\u0430 \u043a\u043e\u0440\u043d\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0441\u0432\u0435\u0434\u0435\u043d\u0430 \u043a \u0437\u0430\u0434\u0430\u0447\u0435 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u0434\u043b\u044f \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c\u044b <a href=\"https:\/\/znanium.ru\/catalog\/document?id=51806\" rel=\"noopener noreferrer nofollow\">\u043b\u0438\u043f\u0448\u0438\u0446\u0435\u0432\u044b \u043c\u0435\u0442\u043e\u0434\u044b<\/a>, \u0442\u0440\u0435\u0431\u0443\u044e\u0449\u0438\u0435 \u043e\u0446\u0435\u043d\u043e\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b.<\/p>\n<p>\u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0435\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0430 \u0440\u0430\u0437\u043d\u043e\u0432\u0438\u0434\u043d\u043e\u0441\u0442\u044c \u043c\u0435\u0442\u043e\u0434\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0437\u0430\u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0449\u0438\u0445 \u043e\u0446\u0435\u043d\u043e\u043a \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439. \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u044d\u0442\u043e\u0439 \u0442\u0435\u0445\u043d\u0438\u043a\u0438 \u0441\u043a\u0430\u043d\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0432\u0441\u0451 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u044e\u0449\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430. \u041f\u043e \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0441 \u043c\u0435\u0442\u043e\u0434\u043e\u043c &#171;\u043b\u0435\u0441\u0435\u043d\u043a\u0438&#187;, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0441\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043a \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0439 \u0431\u0438\u0441\u0435\u043a\u0446\u0438\u0438 \u043f\u043e \u0447\u0435\u0440\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0441\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c, \u043c\u0435\u0442\u043e\u0434 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0443\u0441\u043a\u043e\u0440\u0438\u0442\u044c \u0441\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c.<\/p>\n<h2>\u041f\u0440\u0438\u043c\u0435\u0440<\/h2>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"F_1(x,y)=x+y+\\varphi(x)-0.1,\\\\F_2(x,y)=x+y-\\varphi(x)+0.1,\\\\\\varphi(x)=e^{-x^2}.\" alt=\"F_1(x,y)=x+y+\\varphi(x)-0.1,\\\\F_2(x,y)=x+y-\\varphi(x)+0.1,\\\\\\varphi(x)=e^{-x^2}.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/e9f\/2e2\/16c\/e9f2e216cc6a15917065f68aa92d3204.svg\" width=\"697\" height=\"82\"\/><\/p>\n<details class=\"spoiler\">\n<summary>\u041a\u043e\u0434 \u0434\u043b\u044f \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"matlab\">function ret = phi(x)   ret = exp(-x^2); endfunction  function ret = dphi(x)   ret = -2 * x * exp(-x^2); endfunction  function ret = F1(x, y)   ret = x + y + phi(x) - 0.1; endfunction  function ret = F2(x, y)   ret = x + y - phi(x) + 0.1; endfunction  X = linspace(-3, 3, 100); Y = linspace(-3, 3, 100); [X, Y] = meshgrid(X, Y); Z1 = arrayfun(@F1, X, Y); Z2 = arrayfun(@F2, X, Y); hold on contour(X, Y, Z1, [0 0]) contour(X, Y, Z2, [0 0])<\/code><\/pre>\n<\/p>\n<\/div>\n<\/details>\n<figure class=\"full-width\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/habrastorage.org\/r\/w1560\/getpro\/habr\/upload_files\/dfe\/7bd\/40e\/dfe7bd40e668604c70ce52bd1efc2752.png\" alt=\"\u041b\u0438\u043d\u0438\u0438 \u043d\u0443\u043b\u0435\u0432\u043e\u0433\u043e \u0443\u0440\u043e\u0432\u043d\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439  \" title=\"\u041b\u0438\u043d\u0438\u0438 \u043d\u0443\u043b\u0435\u0432\u043e\u0433\u043e \u0443\u0440\u043e\u0432\u043d\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439  \" width=\"897\" height=\"669\" data-src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/dfe\/7bd\/40e\/dfe7bd40e668604c70ce52bd1efc2752.png\"\/><\/p>\n<div><figcaption>\u041b\u0438\u043d\u0438\u0438 \u043d\u0443\u043b\u0435\u0432\u043e\u0433\u043e \u0443\u0440\u043e\u0432\u043d\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"F_1,F_2\" alt=\"F_1,F_2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/539\/9a3\/166\/5399a3166f1ea8909cedd27c83571576.svg\" width=\"41\" height=\"17\"\/> <\/figcaption><\/div>\n<\/figure>\n<details class=\"spoiler\">\n<summary>\u041a\u043e\u0434 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"matlab\">function [z, jac] = f(p)   x = p(1);   y = p(2);    z(1) = F1(x, y);   z(2) = F2(x, y);   jac(1, 1) = 1 + dphi(x);   jac(1, 2) = 1;   jac(2, 1) = 1 - dphi(x);   jac(2, 2) = 1; endfunction  x_init = [-0.5; 0.5]; [sol, fval, info] = fsolve (@f, x_init, optimset (\"jacobian\", \"on\")) x_init = [0.5; 0.5]; [sol, fval, info] = fsolve (@f, x_init, optimset (\"jacobian\", \"on\")) x_init = [0; 0]; [sol, fval, info] = fsolve (@f, x_init, optimset (\"jacobian\", \"on\")) <\/code><\/pre>\n<\/p>\n<\/div>\n<\/details>\n<p>\u0417\u0430\u043f\u0443\u0441\u0442\u0438\u043c \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0439 \u0440\u0435\u0448\u0430\u0442\u0435\u043b\u044c <code>fsolve<\/code> (\u0441\u0440\u0435\u0434\u0430 Octave).<\/p>\n<p>\u041f\u0440\u0438 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"x=-0.5,y=0.5\" alt=\"x=-0.5,y=0.5\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/dc0\/082\/216\/dc00822164f13f546a29e955b40994c5.svg\" width=\"145\" height=\"19\"\/> \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043a\u043e\u0440\u0435\u043d\u044c <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"(-1.5174, 1.5174)\" alt=\"(-1.5174, 1.5174)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/b6d\/cf4\/bd5\/b6dcf4bd570dfdb886f9a0e63d4c464c.svg\" width=\"146\" height=\"22\"\/>.<\/p>\n<p>\u041f\u0440\u0438 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"x=0.5,y=0.5\" alt=\"x=0.5,y=0.5\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c6c\/ebc\/6f8\/c6cebc6f8c946c8bad2a01a59ea9dac1.svg\" width=\"130\" height=\"19\"\/> \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043a\u043e\u0440\u0435\u043d\u044c <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"(1.5174, -1.5174)\" alt=\"(1.5174, -1.5174)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f3f\/eb0\/672\/f3feb0672159f5aae67c5a898f3bb4d2.svg\" width=\"146\" height=\"22\"\/>.<\/p>\n<p>\u041f\u0440\u0438 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"x=0,y=0\" alt=\"x=0,y=0\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/c47\/ea8\/713\/c47ea87130196aa4be5e9b15e60cbee4.svg\" width=\"100\" height=\"19\"\/> \u044f\u043a\u043e\u0431\u0438\u0430\u043d \u0432\u044b\u0440\u043e\u0436\u0434\u0430\u0435\u0442\u0441\u044f, \u0438 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043d\u0435 \u043d\u0430\u0445\u043e\u0434\u0438\u0442 \u043a\u043e\u0440\u043d\u044f.<\/p>\n<h2>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c<\/h2>\n<p>\u0414\u043e\u043f\u0443\u0441\u0442\u0438\u043c, \u0447\u0442\u043e \u043d\u0430\u043c \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b \u043e\u0446\u0435\u043d\u043a\u0438 \u0441\u043d\u0438\u0437\u0443 \u0438 \u0441\u0432\u0435\u0440\u0445\u0443 \u0434\u043b\u044f \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u044b:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\widehat M_{ji} \\leq \\frac{\\partial F_j(\\mathbf x)}{\\partial x_i}\\leq \\widetilde M_{ji},\" alt=\"\\widehat M_{ji} \\leq \\frac{\\partial F_j(\\mathbf x)}{\\partial x_i}\\leq \\widetilde M_{ji},\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/cf5\/d3e\/b61\/cf5d3eb61c4c761feaf8f36ca8eb3934.svg\" width=\"191\" height=\"49\"\/><\/p>\n<p>\u043f\u0440\u0438\u0447\u0435\u043c \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\widehat M, \\widetilde M\" alt=\"\\widehat M, \\widetilde M\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/f17\/c21\/7d5\/f17c217d5c6fb0075b48fbe9110e2ef6.svg\" width=\"53\" height=\"25\"\/> \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u043d\u0443\u0436\u043d\u044b\u043c\u0438 \u043d\u0430\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438 (\u043e\u0431 \u044d\u0442\u043e\u043c \u0434\u0430\u043b\u044c\u0448\u0435).<\/p>\n<p>\u041f\u0443\u0441\u0442\u044c <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf x^{(k)}\" alt=\"\\mathbf x^{(k)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/dd4\/c8f\/6c3\/dd4c8f6c3e8893d2fef8ec186e434350.svg\" width=\"31\" height=\"22\"\/> &#8212; \u0442\u0435\u043a\u0443\u0449\u0435\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"F_1\" alt=\"F_1\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/d45\/de4\/8e9\/d45de48e9c73c208f7e2bd36af1efffe.svg\" width=\"21\" height=\"19\"\/> \u0438 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"F_2\" alt=\"F_2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/24e\/a3f\/409\/24ea3f4097afb9389ce6220ab8bbc9bc.svg\" width=\"21\" height=\"19\"\/> \u0438\u043c\u0435\u044e\u0442 \u0440\u0430\u0437\u043d\u044b\u0435 \u0437\u043d\u0430\u043a\u0438 (\u043d\u0430 \u0440\u0438\u0441\u0443\u043d\u043a\u0435 \u0442\u0430\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0431\u0443\u0434\u0435\u0442 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c\u0441\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043a\u0440\u0438\u0432\u044b\u043c\u0438). \u0422\u043e\u0433\u0434\u0430, \u0447\u0442\u043e\u0431\u044b, \u0432\u043e-\u043f\u0435\u0440\u0432\u044b\u0445, \u0437\u0430\u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 (\u0432\u043b\u0435\u0432\u043e-\u0432\u0432\u0435\u0440\u0445 \u0438\u043b\u0438 \u0432\u043f\u0440\u0430\u0432\u043e-\u0432\u043d\u0438\u0437) \u0438, \u0432\u043e-\u0432\u0442\u043e\u0440\u044b\u0445, \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"\\mathbf x^{(k+1)}\" alt=\"\\mathbf x^{(k+1)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0d3\/8a1\/5eb\/0d38a15ebe09d85139c250f351d01072.svg\" width=\"49\" height=\"22\"\/> \u043e\u0441\u0442\u0430\u043d\u0435\u0442\u0441\u044f \u0432 \u0442\u043e\u0439 \u0436\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0438 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u043a\u043e\u0447\u0435\u0442 \u043a\u043e\u0440\u0435\u043d\u044c, \u043e\u0446\u0435\u043d\u0438\u043c \u043f\u0440\u0438\u0440\u0430\u0449\u0435\u043d\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"F_1,F_2\" alt=\"F_1,F_2\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/180\/321\/e96\/180321e96ff666209b7fde95a6209047.svg\" width=\"51\" height=\"20\"\/> \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0438\u0440\u0430\u0449\u0435\u043d\u0438\u0439. \u041f\u043e\u043b\u0443\u0447\u0438\u043c<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"F_1(\\mathbf x^{(k+1)})=F_1(\\mathbf x^{(k)})+\\frac{\\partial F_1(\\widetilde {\\mathbf x})}{\\partial x}(x^{(k+1)}-x^{(k)})+\\frac{\\partial F_1(\\widetilde {\\mathbf x})}{\\partial y}(y^{(k+1)}-y^{(k)}),\\\\F_2(\\mathbf x^{(k+1)})=F_2(\\mathbf x^{(k)})+\\frac{\\partial F_2(\\widehat {\\mathbf x})}{\\partial x}(x^{(k+1)}-x^{(k)})+\\frac{\\partial F_2(\\widehat {\\mathbf x})}{\\partial y}(y^{(k+1)}-y^{(k)}).\" alt=\"F_1(\\mathbf x^{(k+1)})=F_1(\\mathbf x^{(k)})+\\frac{\\partial F_1(\\widetilde {\\mathbf x})}{\\partial x}(x^{(k+1)}-x^{(k)})+\\frac{\\partial F_1(\\widetilde {\\mathbf x})}{\\partial y}(y^{(k+1)}-y^{(k)}),\\\\F_2(\\mathbf x^{(k+1)})=F_2(\\mathbf x^{(k)})+\\frac{\\partial F_2(\\widehat {\\mathbf x})}{\\partial x}(x^{(k+1)}-x^{(k)})+\\frac{\\partial F_2(\\widehat {\\mathbf x})}{\\partial y}(y^{(k+1)}-y^{(k)}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0ae\/197\/6d1\/0ae1976d15e8c3fa455bad4fffc20596.svg\" width=\"697\" height=\"103\"\/><\/p>\n<p>\u0422\u043e\u0433\u0434\u0430, \u0435\u0441\u043b\u0438 \u043c\u044b \u0445\u043e\u0442\u0438\u043c, \u0447\u0442\u043e\u0431\u044b \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0434\u0432\u0438\u0433\u0430\u043b\u0441\u044f \u0432\u043b\u0435\u0432\u043e-\u0432\u0432\u0435\u0440\u0445, \u0442\u043e \u0435\u0441\u0442\u044c <img class=\"formula inline\" source=\"x^{(k+1)}&lt;x^{(k)}, \\; y^{(k+1)}>y^{(k)}&#187; alt=&#187;x^{(k+1)}&lt;x^{(k)}, \\; y^{(k+1)}>y^{(k)}&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/178\/205\/a08\/178205a084858b4cf83ba2237cdeb93d.svg&#187; width=&#187;220&#8243; height=&#187;25&#8243;\/>, \u0442\u043e \u0434\u043b\u044f \u0441\u043e\u0445\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 <img class=\"formula inline\" source=\"F_1>0,F_2&lt;0&#8243; alt=&#187;F_1>0,F_2&lt;0&#8243; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/1c5\/bc7\/5fe\/1c5bc75fea938b04d179f66e5677ad83.svg&#187; width=&#187;122&#8243; height=&#187;20&#8243;\/> \u043d\u0443\u0436\u043d\u043e \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u043d\u0438\u0437\u0443 \u0438 \u0441\u0432\u0435\u0440\u0445\u0443:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"F_1(\\mathbf x^{(k+1)})\\geq F_1(\\mathbf x^{(k)})+\\widetilde M_{11}(x^{(k+1)}-x^{(k)})+\\widehat M_{12} (y^{(k+1)}-y^{(k)}),\\\\F_2(\\mathbf x^{(k+1)})\\leq F_2(\\mathbf x^{(k)})+\\widehat M_{21}(x^{(k+1)}-x^{(k)})+\\widetilde M_{22}(y^{(k+1)}-y^{(k)}).\" alt=\"F_1(\\mathbf x^{(k+1)})\\geq F_1(\\mathbf x^{(k)})+\\widetilde M_{11}(x^{(k+1)}-x^{(k)})+\\widehat M_{12} (y^{(k+1)}-y^{(k)}),\\\\F_2(\\mathbf x^{(k+1)})\\leq F_2(\\mathbf x^{(k)})+\\widehat M_{21}(x^{(k+1)}-x^{(k)})+\\widetilde M_{22}(y^{(k+1)}-y^{(k)}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/26b\/99f\/2fd\/26b99f2fd3a4efd1da13fe974caf5588.svg\" width=\"697\" height=\"58\"\/><\/p>\n<p>\u0417\u043d\u0430\u0447\u0438\u0442, \u0435\u0441\u043b\u0438 \u043c\u044b \u0440\u0435\u0448\u0438\u043c \u0442\u0430\u043a\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\widetilde M_{11}(x^{(k+1)}-x^{(k)})+\\widehat M_{12} (y^{(k+1)}-y^{(k)}) = -F_1(\\mathbf x^{(k)}),\\\\\\widehat M_{21}(x^{(k+1)}-x^{(k)})+\\widetilde M_{22}(y^{(k+1)}-y^{(k)}) = -F_2(\\mathbf x^{(k)})\" alt=\"\\widetilde M_{11}(x^{(k+1)}-x^{(k)})+\\widehat M_{12} (y^{(k+1)}-y^{(k)}) = -F_1(\\mathbf x^{(k)}),\\\\\\widehat M_{21}(x^{(k+1)}-x^{(k)})+\\widetilde M_{22}(y^{(k+1)}-y^{(k)}) = -F_2(\\mathbf x^{(k)})\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/467\/3d2\/b0c\/4673d2b0c082b55a8dec6561d137ce08.svg\" width=\"697\" height=\"58\"\/><\/p>\n<p>\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"x^{(k+1)},y^{(k+1)}\" alt=\"x^{(k+1)},y^{(k+1)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/bd1\/299\/a9b\/bd1299a9b8a1f7df97c1198a8c821e5d.svg\" width=\"103\" height=\"25\"\/>, \u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u043c, \u0447\u0442\u043e<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"F_1(\\mathbf x^{(k+1)})\\geq 0, \\; F_2(\\mathbf x^{(k+1})\\leq 0.\" alt=\"F_1(\\mathbf x^{(k+1)})\\geq 0, \\; F_2(\\mathbf x^{(k+1})\\leq 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/fdb\/8f6\/412\/fdb8f64128dc077a3f666a00143c6721.svg\" width=\"255\" height=\"26\"\/><\/p>\n<p>\u041d\u043e \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0443\u0436\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u043e\u0432\u0430\u043b\u043e \u0432\u044b\u0431\u0440\u0430\u043d\u043d\u043e\u043c\u0443 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044e <img class=\"formula inline\" source=\"x^{(k+1)}&lt;x^{(k)},\\; y^{(k+1)}>y^{(k)}&#187; alt=&#187;x^{(k+1)}&lt;x^{(k)},\\; y^{(k+1)}>y^{(k)}&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/bff\/812\/1ef\/bff8121eff60a15f9dcd237ba99acf61.svg&#187; width=&#187;220&#8243; height=&#187;25&#8243;\/>. \u042d\u0442\u043e \u0431\u0443\u0434\u0435\u0442 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442\u043e \u043f\u0440\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043e\u0440\u0438\u0435\u043d\u0442\u0430\u0446\u0438\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0430 \u0438\u043c\u0435\u043d\u043d\u043e \u043a\u043e\u0433\u0434\u0430  <\/p>\n<p><img class=\"formula\" source=\"\\left|\\matrix{\\widetilde M_{11} &amp; \\widehat M_{12}\\\\ \\widehat M_{21} &amp; \\widetilde M_{22}}\\right| > 0.&#187; alt=&#187;\\left|\\matrix{\\widetilde M_{11} &amp; \\widehat M_{12}\\\\ \\widehat M_{21} &amp; \\widetilde M_{22}}\\right| > 0.&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/a00\/fae\/c94\/a00faec94682a5ed3f980a106c1f669b.svg&#187; width=&#187;153&#8243; height=&#187;56&#8243;\/><\/p>\n<p>\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u0432 \u0441\u043b\u0443\u0447\u0430\u0435 <img class=\"formula inline\" source=\"x^{(k+1)}>x^{(k)},\\; y^{(k+1)}&lt;y^{(k)}&#187; alt=&#187;x^{(k+1)}>x^{(k)},\\; y^{(k+1)}&lt;y^{(k)}&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0cf\/661\/2bf\/0cf6612bfcedcfbb36c08c6f08c330eb.svg&#187; width=&#187;220&#8243; height=&#187;25&#8243;\/>, \u0440\u0435\u0448\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0443:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\widehat M_{11}(x^{(k+1)}-x^{(k)})+\\widetilde M_{12} (y^{(k+1)}-y^{(k)}) = -F_1(\\mathbf x^{(k)}),\\\\\\widetilde M_{21}(x^{(k+1)}-x^{(k)})+\\widehat M_{22}(y^{(k+1)}-y^{(k)}) = -F_2(\\mathbf x^{(k)}) \" alt=\"\\widehat M_{11}(x^{(k+1)}-x^{(k)})+\\widetilde M_{12} (y^{(k+1)}-y^{(k)}) = -F_1(\\mathbf x^{(k)}),\\\\\\widetilde M_{21}(x^{(k+1)}-x^{(k)})+\\widehat M_{22}(y^{(k+1)}-y^{(k)}) = -F_2(\\mathbf x^{(k)}) \" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/238\/0f9\/4c1\/2380f94c10b745a69ead3f264ed1222d.svg\" width=\"697\" height=\"58\"\/><\/p>\n<p>\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"x^{(k+1)},y^{(k+1)}\" alt=\"x^{(k+1)},y^{(k+1)}\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/bd1\/299\/a9b\/bd1299a9b8a1f7df97c1198a8c821e5d.svg\" width=\"103\" height=\"25\"\/>, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c, \u0447\u0442\u043e<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"F_1(\\mathbf x^{(k+1)})\\leq 0, \\; F_2(\\mathbf x^{(k+1})\\geq 0.\" alt=\"F_1(\\mathbf x^{(k+1)})\\leq 0, \\; F_2(\\mathbf x^{(k+1})\\geq 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/37a\/c65\/31c\/37ac6531c55da4708081eb9125960bec.svg\" width=\"255\" height=\"26\"\/><\/p>\n<p>\u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"F_1(\\mathbf x^{(k+1)})\\leq F_1(\\mathbf x^{(k)})+\\widehat M_{11}(x^{(k+1)}-x^{(k)})+\\widetilde M_{12} (y^{(k+1)}-y^{(k)}),\\\\F_2(\\mathbf x^{(k+1)})\\geq F_2(\\mathbf x^{(k)})+\\widetilde M_{21}(x^{(k+1)}-x^{(k)})+\\widehat M_{22}(y^{(k+1)}-y^{(k)}).\" alt=\"F_1(\\mathbf x^{(k+1)})\\leq F_1(\\mathbf x^{(k)})+\\widehat M_{11}(x^{(k+1)}-x^{(k)})+\\widetilde M_{12} (y^{(k+1)}-y^{(k)}),\\\\F_2(\\mathbf x^{(k+1)})\\geq F_2(\\mathbf x^{(k)})+\\widetilde M_{21}(x^{(k+1)}-x^{(k)})+\\widehat M_{22}(y^{(k+1)}-y^{(k)}).\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/6ba\/d97\/e26\/6bad97e2615e831934ab549655ab154b.svg\" width=\"697\" height=\"58\"\/><\/p>\n<p>\u041f\u0440\u0438 \u044d\u0442\u043e\u043c \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"formula\" source=\"\\left|\\matrix{\\widehat M_{11} &amp; \\widetilde M_{12}\\\\ \\widetilde M_{21} &amp; \\widehat M_{22}}\\right| &lt; 0.\" alt=\"\\left|\\matrix{\\widehat M_{11} &amp; \\widetilde M_{12}\\\\ \\widetilde M_{21} &amp; \\widehat M_{22}}\\right| &lt; 0.\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/69c\/ab0\/41c\/69cab041cb9a0a58c94b3e4307baa884.svg\" width=\"153\" height=\"56\"\/><\/p>\n<p>\u0417\u0430\u043f\u0443\u0441\u0442\u0438\u043c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u0430.<\/p>\n<details class=\"spoiler\">\n<summary>\u041a\u043e\u0434 \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"matlab\"># \u043e\u0446\u0435\u043d\u043a\u0438 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 J_upper = [2, 1; 2, 1]; J_lower = [0, 1; 0, 1]; Q1 = [J_upper(1, 1), J_lower(1, 2); J_lower(2, 1), J_upper(2, 2)]; Q2 = [J_lower(1, 1), J_upper(1, 2); J_upper(2, 1), J_lower(2, 2)];  # \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0434\u0435\u0442 \u0432\u043b\u0435\u0432\u043e-\u0432\u0432\u0435\u0440\u0445 disp(\"Algorithm 1\") num_iter = 30; x = x_init; for i = 1:num_iter   x -= Q1 ^ -1 * [F1(x(1), x(2)); F2(x(1), x(2))] endfor  # \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0434\u0435\u0442 \u0432\u043f\u0440\u0430\u0432\u043e-\u0432\u043d\u0438\u0437 disp(\"Algorithm 2\") x = x_init; for i = 1:num_iter   x -= Q2 ^ -1 * [F1(x(1), x(2)); F2(x(1), x(2))] endfor<\/code><\/pre>\n<\/p>\n<\/div>\n<\/details>\n<p>\u041f\u043e\u043b\u0443\u0447\u0438\u043c \u0432 \u043e\u0434\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043a\u043e\u0440\u0435\u043d\u044c <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"(-1.5174, 1.5174)\" alt=\"(-1.5174, 1.5174)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/ffa\/08a\/06a\/ffa08a06a789fa4ff8df7164b21bbd50.svg\" width=\"146\" height=\"22\"\/>, \u0432 \u0434\u0440\u0443\u0433\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043a\u043e\u0440\u0435\u043d\u044c <img loading=\"lazy\" decoding=\"async\" class=\"formula inline\" source=\"(1.5174, -1.5174)\" alt=\"(1.5174, -1.5174)\" src=\"https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/da9\/b92\/913\/da9b92913ec9d396b1eabe5d6ed79fd3.svg\" width=\"146\" height=\"22\"\/> \u0437\u0430 30 \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0439.<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 \u043c\u043d\u043e\u0433\u043e\u043a\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0441\u0440\u0430\u0432\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u0440\u0443\u0434\u043e\u0435\u043c\u043a\u043e\u0433\u043e \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043c\u0435\u0442\u043e\u0434\u0430 \u0431\u0438\u0441\u0435\u043a\u0446\u0438\u0438 \u0432 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0435 &#171;\u043b\u0435\u0441\u0435\u043d\u043a\u0430&#187;.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!----><!----><\/div>\n<p><!----><!----><br \/> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/articles\/787454\/\"> https:\/\/habr.com\/ru\/articles\/787454\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<div><!--[--><!--]--><\/div>\n<div id=\"post-content-body\">\n<div>\n<div class=\"article-formatted-body article-formatted-body article-formatted-body_version-2\">\n<div xmlns=\"http:\/\/www.w3.org\/1999\/xhtml\">\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u0438\u0441\u0442\u0435\u043c\u0443 \u0438\u0437 \u0434\u0432\u0443\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439 , \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0449\u0443\u044e \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u043e\u043c \u043f\u043e\u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u043d\u043e\u0439 \u043c\u043e\u043d\u043e\u0442\u043e\u043d\u043d\u043e\u0441\u0442\u0438: \u0441 \u0440\u043e\u0441\u0442\u043e\u043c  \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \u0442\u0430\u043a\u0436\u0435 \u0440\u0430\u0441\u0442\u0443\u0442. \u0417\u0430\u0434\u0430\u0447\u0430 \u0441\u043e\u0441\u0442\u043e\u0438\u0442 \u0432 \u043d\u0430\u0445\u043e\u0436\u0434\u0435\u043d\u0438\u0438 \u0432\u0441\u0435\u0445 \u043a\u043e\u0440\u043d\u0435\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b.<\/p>\n<h2>\u0412\u0432\u0435\u0434\u0435\u043d\u0438\u0435<\/h2>\n<p>\u0414\u0432\u0443\u043c\u0435\u0440\u043d\u044b\u0439 \u043c\u0435\u0442\u043e\u0434 \u0431\u0438\u0441\u0435\u043a\u0446\u0438\u0438 \u043e\u0431\u0441\u0443\u0436\u0434\u0430\u043b\u0441\u044f <a href=\"https:\/\/stackoverflow.com\/questions\/3513660\/multivariate-bisection-method\" rel=\"noopener noreferrer nofollow\">\u0437\u0434\u0435\u0441\u044c<\/a>. \u0412\u043e\u043e\u0431\u0449\u0435 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u043c\u043d\u043e\u0433\u043e\u043c\u0435\u0440\u043d\u044b\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0432\u043e\u0437\u043c\u043e\u0436\u0435\u043d <a href=\"https:\/\/shop.rcd.ru\/catalog\/intervalnyy-analiz-i-ego-prilojeniya\/16552\/\" rel=\"noopener noreferrer nofollow\">\u043c\u0435\u0442\u043e\u0434 \u0432\u0435\u0442\u0432\u0435\u0439 \u0438 \u0433\u0440\u0430\u043d\u0438\u0446<\/a>, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u044e\u0449\u0430\u044f \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u0440\u0430\u0437\u0431\u0438\u0432\u0430\u0435\u0442\u0441\u044f \u043d\u0430 \u0447\u0430\u0441\u0442\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e \u043e\u0442\u0431\u0440\u0430\u0441\u044b\u0432\u0430\u044e\u0442\u0441\u044f, \u043a\u043e\u0433\u0434\u0430 \u043e\u043d\u0438 \u043d\u0435 \u0443\u0434\u043e\u0432\u043b\u0435\u0442\u0432\u043e\u0440\u044f\u044e\u0442 \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u043c \u0443\u0441\u043b\u043e\u0432\u0438\u044f\u043c \u043d\u0430\u043b\u0438\u0447\u0438\u044f \u0432 \u043d\u0438\u0445 \u043a\u043e\u0440\u043d\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b. \u0422\u0430\u043a\u0436\u0435 \u0441\u0442\u043e\u0438\u0442 \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u0437\u0430\u0434\u0430\u0447\u0430 \u043f\u043e\u0438\u0441\u043a\u0430 \u043a\u043e\u0440\u043d\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u043c\u043e\u0436\u0435\u0442 \u0431\u044b\u0442\u044c \u0441\u0432\u0435\u0434\u0435\u043d\u0430 \u043a \u0437\u0430\u0434\u0430\u0447\u0435 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0439 \u043e\u043f\u0442\u0438\u043c\u0438\u0437\u0430\u0446\u0438\u0438, \u0434\u043b\u044f \u043a\u043e\u0442\u043e\u0440\u043e\u0439 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c\u044b <a href=\"https:\/\/znanium.ru\/catalog\/document?id=51806\" rel=\"noopener noreferrer nofollow\">\u043b\u0438\u043f\u0448\u0438\u0446\u0435\u0432\u044b \u043c\u0435\u0442\u043e\u0434\u044b<\/a>, \u0442\u0440\u0435\u0431\u0443\u044e\u0449\u0438\u0435 \u043e\u0446\u0435\u043d\u043e\u043a \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b.<\/p>\n<p>\u0412 \u043d\u0430\u0441\u0442\u043e\u044f\u0449\u0435\u0439 \u0441\u0442\u0430\u0442\u044c\u0435 \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u0430 \u0440\u0430\u0437\u043d\u043e\u0432\u0438\u0434\u043d\u043e\u0441\u0442\u044c \u043c\u0435\u0442\u043e\u0434\u0430 \u041d\u044c\u044e\u0442\u043e\u043d\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0437\u0430\u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u043f\u043e\u0434\u0445\u043e\u0434\u044f\u0449\u0438\u0445 \u043e\u0446\u0435\u043d\u043e\u043a \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439. \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u044d\u0442\u043e\u0439 \u0442\u0435\u0445\u043d\u0438\u043a\u0438 \u0441\u043a\u0430\u043d\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0432\u0441\u0451 \u0438\u043d\u0442\u0435\u0440\u0435\u0441\u0443\u044e\u0449\u0435\u0435 \u043f\u0440\u043e\u0441\u0442\u0440\u0430\u043d\u0441\u0442\u0432\u043e \u043f\u043e\u0438\u0441\u043a\u0430. \u041f\u043e \u0441\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044e \u0441 \u043c\u0435\u0442\u043e\u0434\u043e\u043c &#171;\u043b\u0435\u0441\u0435\u043d\u043a\u0438&#187;, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0434\u0432\u0443\u043c\u0435\u0440\u043d\u0430\u044f \u0437\u0430\u0434\u0430\u0447\u0430 \u0441\u0432\u043e\u0434\u0438\u0442\u0441\u044f \u043a \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0439 \u0431\u0438\u0441\u0435\u043a\u0446\u0438\u0438 \u043f\u043e \u0447\u0435\u0440\u0435\u0434\u0443\u044e\u0449\u0438\u043c\u0441\u044f \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u0430\u043c, \u043c\u0435\u0442\u043e\u0434 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0443\u0441\u043a\u043e\u0440\u0438\u0442\u044c \u0441\u0445\u043e\u0434\u0438\u043c\u043e\u0441\u0442\u044c.<\/p>\n<h2>\u041f\u0440\u0438\u043c\u0435\u0440<\/h2>\n<p>\u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443:<\/p>\n<details class=\"spoiler\">\n<summary>\u041a\u043e\u0434 \u0434\u043b\u044f \u0432\u0438\u0437\u0443\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"matlab\">function ret = phi(x)   ret = exp(-x^2); endfunction  function ret = dphi(x)   ret = -2 * x * exp(-x^2); endfunction  function ret = F1(x, y)   ret = x + y + phi(x) - 0.1; endfunction  function ret = F2(x, y)   ret = x + y - phi(x) + 0.1; endfunction  X = linspace(-3, 3, 100); Y = linspace(-3, 3, 100); [X, Y] = meshgrid(X, Y); Z1 = arrayfun(@F1, X, Y); Z2 = arrayfun(@F2, X, Y); hold on contour(X, Y, Z1, [0 0]) contour(X, Y, Z2, [0 0])<\/code><\/pre>\n<\/p>\n<\/div>\n<\/details>\n<figure class=\"full-width\">\n<div><figcaption>\u041b\u0438\u043d\u0438\u0438 \u043d\u0443\u043b\u0435\u0432\u043e\u0433\u043e \u0443\u0440\u043e\u0432\u043d\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0439  <\/figcaption><\/div>\n<\/figure>\n<details class=\"spoiler\">\n<summary>\u041a\u043e\u0434 \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"matlab\">function [z, jac] = f(p)   x = p(1);   y = p(2);    z(1) = F1(x, y);   z(2) = F2(x, y);   jac(1, 1) = 1 + dphi(x);   jac(1, 2) = 1;   jac(2, 1) = 1 - dphi(x);   jac(2, 2) = 1; endfunction  x_init = [-0.5; 0.5]; [sol, fval, info] = fsolve (@f, x_init, optimset (\"jacobian\", \"on\")) x_init = [0.5; 0.5]; [sol, fval, info] = fsolve (@f, x_init, optimset (\"jacobian\", \"on\")) x_init = [0; 0]; [sol, fval, info] = fsolve (@f, x_init, optimset (\"jacobian\", \"on\")) <\/code><\/pre>\n<\/p>\n<\/div>\n<\/details>\n<p>\u0417\u0430\u043f\u0443\u0441\u0442\u0438\u043c \u0441\u0442\u0430\u043d\u0434\u0430\u0440\u0442\u043d\u044b\u0439 \u0440\u0435\u0448\u0430\u0442\u0435\u043b\u044c <code>fsolve<\/code> (\u0441\u0440\u0435\u0434\u0430 Octave).<\/p>\n<p>\u041f\u0440\u0438 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438  \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043a\u043e\u0440\u0435\u043d\u044c .<\/p>\n<p>\u041f\u0440\u0438 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438  \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u043a\u043e\u0440\u0435\u043d\u044c .<\/p>\n<p>\u041f\u0440\u0438 \u043d\u0430\u0447\u0430\u043b\u044c\u043d\u043e\u043c \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0438  \u044f\u043a\u043e\u0431\u0438\u0430\u043d \u0432\u044b\u0440\u043e\u0436\u0434\u0430\u0435\u0442\u0441\u044f, \u0438 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043d\u0435 \u043d\u0430\u0445\u043e\u0434\u0438\u0442 \u043a\u043e\u0440\u043d\u044f.<\/p>\n<h2>\u0410\u043b\u0433\u043e\u0440\u0438\u0442\u043c<\/h2>\n<p>\u0414\u043e\u043f\u0443\u0441\u0442\u0438\u043c, \u0447\u0442\u043e \u043d\u0430\u043c \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b \u043e\u0446\u0435\u043d\u043a\u0438 \u0441\u043d\u0438\u0437\u0443 \u0438 \u0441\u0432\u0435\u0440\u0445\u0443 \u0434\u043b\u044f \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u043e\u0432 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u044b:<\/p>\n<p>\u043f\u0440\u0438\u0447\u0435\u043c \u043d\u0435\u043e\u0442\u0440\u0438\u0446\u0430\u0442\u0435\u043b\u044c\u043d\u044b\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b  \u043e\u0431\u043b\u0430\u0434\u0430\u044e\u0442 \u043d\u0443\u0436\u043d\u044b\u043c\u0438 \u043d\u0430\u043c \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438 (\u043e\u0431 \u044d\u0442\u043e\u043c \u0434\u0430\u043b\u044c\u0448\u0435).<\/p>\n<p>\u041f\u0443\u0441\u0442\u044c  &#8212; \u0442\u0435\u043a\u0443\u0449\u0435\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435, \u0432 \u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u0438  \u0438  \u0438\u043c\u0435\u044e\u0442 \u0440\u0430\u0437\u043d\u044b\u0435 \u0437\u043d\u0430\u043a\u0438 (\u043d\u0430 \u0440\u0438\u0441\u0443\u043d\u043a\u0435 \u0442\u0430\u043a\u0430\u044f \u0442\u043e\u0447\u043a\u0430 \u0431\u0443\u0434\u0435\u0442 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u044c\u0441\u044f \u043c\u0435\u0436\u0434\u0443 \u0434\u0432\u0443\u043c\u044f \u043a\u0440\u0438\u0432\u044b\u043c\u0438). \u0422\u043e\u0433\u0434\u0430, \u0447\u0442\u043e\u0431\u044b, \u0432\u043e-\u043f\u0435\u0440\u0432\u044b\u0445, \u0437\u0430\u0444\u0438\u043a\u0441\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u0435 \u0434\u0432\u0438\u0436\u0435\u043d\u0438\u044f \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0430 (\u0432\u043b\u0435\u0432\u043e-\u0432\u0432\u0435\u0440\u0445 \u0438\u043b\u0438 \u0432\u043f\u0440\u0430\u0432\u043e-\u0432\u043d\u0438\u0437) \u0438, \u0432\u043e-\u0432\u0442\u043e\u0440\u044b\u0445, \u0433\u0430\u0440\u0430\u043d\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435 \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u0435  \u043e\u0441\u0442\u0430\u043d\u0435\u0442\u0441\u044f \u0432 \u0442\u043e\u0439 \u0436\u0435 \u043e\u0431\u043b\u0430\u0441\u0442\u0438 \u0438 \u043d\u0435 \u043f\u0435\u0440\u0435\u0441\u043a\u043e\u0447\u0435\u0442 \u043a\u043e\u0440\u0435\u043d\u044c, \u043e\u0446\u0435\u043d\u0438\u043c \u043f\u0440\u0438\u0440\u0430\u0449\u0435\u043d\u0438\u0435 \u0437\u043d\u0430\u0447\u0435\u043d\u0438\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0439  \u043f\u043e \u0444\u043e\u0440\u043c\u0443\u043b\u0435 \u043a\u043e\u043d\u0435\u0447\u043d\u044b\u0445 \u043f\u0440\u0438\u0440\u0430\u0449\u0435\u043d\u0438\u0439. \u041f\u043e\u043b\u0443\u0447\u0438\u043c<\/p>\n<p>\u0422\u043e\u0433\u0434\u0430, \u0435\u0441\u043b\u0438 \u043c\u044b \u0445\u043e\u0442\u0438\u043c, \u0447\u0442\u043e\u0431\u044b \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0434\u0432\u0438\u0433\u0430\u043b\u0441\u044f \u0432\u043b\u0435\u0432\u043e-\u0432\u0432\u0435\u0440\u0445, \u0442\u043e \u0435\u0441\u0442\u044c y^{(k)}&#187; alt=&#187;x^{(k+1)}&lt;x^{(k)}, \\; y^{(k+1)}>y^{(k)}&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/178\/205\/a08\/178205a084858b4cf83ba2237cdeb93d.svg&#187; width=&#187;220&#8243; height=&#187;25&#8243;\/>, \u0442\u043e \u0434\u043b\u044f \u0441\u043e\u0445\u0440\u0430\u043d\u0435\u043d\u0438\u044f \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 0,F_2&lt;0&#8243; alt=&#187;F_1>0,F_2&lt;0&#8243; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/1c5\/bc7\/5fe\/1c5bc75fea938b04d179f66e5677ad83.svg&#187; width=&#187;122&#8243; height=&#187;20&#8243;\/> \u043d\u0443\u0436\u043d\u043e \u043e\u0446\u0435\u043d\u0438\u0442\u044c \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u044b \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u043d\u0438\u0437\u0443 \u0438 \u0441\u0432\u0435\u0440\u0445\u0443:<\/p>\n<p>\u0417\u043d\u0430\u0447\u0438\u0442, \u0435\u0441\u043b\u0438 \u043c\u044b \u0440\u0435\u0448\u0438\u043c \u0442\u0430\u043a\u0443\u044e \u0441\u0438\u0441\u0442\u0435\u043c\u0443:<\/p>\n<p>\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e , \u0442\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u043c, \u0447\u0442\u043e<\/p>\n<p>\u041d\u043e \u0434\u043b\u044f \u044d\u0442\u043e\u0433\u043e \u043d\u0443\u0436\u043d\u043e, \u0447\u0442\u043e\u0431\u044b \u0440\u0435\u0448\u0435\u043d\u0438\u0435 \u0434\u0430\u043d\u043d\u043e\u0439 \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0441\u0438\u0441\u0442\u0435\u043c\u044b \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u043e\u0432\u0430\u043b\u043e \u0432\u044b\u0431\u0440\u0430\u043d\u043d\u043e\u043c\u0443 \u043d\u0430\u043f\u0440\u0430\u0432\u043b\u0435\u043d\u0438\u044e y^{(k)}&#187; alt=&#187;x^{(k+1)}&lt;x^{(k)},\\; y^{(k+1)}>y^{(k)}&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/bff\/812\/1ef\/bff8121eff60a15f9dcd237ba99acf61.svg&#187; width=&#187;220&#8243; height=&#187;25&#8243;\/>. \u042d\u0442\u043e \u0431\u0443\u0434\u0435\u0442 \u0434\u043e\u0441\u0442\u0438\u0433\u043d\u0443\u0442\u043e \u043f\u0440\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u043d\u043e\u0439 \u043e\u0440\u0438\u0435\u043d\u0442\u0430\u0446\u0438\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043e\u0432, \u0430 \u0438\u043c\u0435\u043d\u043d\u043e \u043a\u043e\u0433\u0434\u0430  <\/p>\n<p> 0.&#187; alt=&#187;\\left|\\matrix{\\widetilde M_{11} &amp; \\widehat M_{12}\\\\ \\widehat M_{21} &amp; \\widetilde M_{22}}\\right| > 0.&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/a00\/fae\/c94\/a00faec94682a5ed3f980a106c1f669b.svg&#187; width=&#187;153&#8243; height=&#187;56&#8243;\/><\/p>\n<p>\u0410\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u0432 \u0441\u043b\u0443\u0447\u0430\u0435 x^{(k)},\\; y^{(k+1)}&lt;y^{(k)}&#187; alt=&#187;x^{(k+1)}>x^{(k)},\\; y^{(k+1)}&lt;y^{(k)}&#187; src=&#187;https:\/\/habrastorage.org\/getpro\/habr\/upload_files\/0cf\/661\/2bf\/0cf6612bfcedcfbb36c08c6f08c330eb.svg&#187; width=&#187;220&#8243; height=&#187;25&#8243;\/>, \u0440\u0435\u0448\u0430\u044f \u0441\u0438\u0441\u0442\u0435\u043c\u0443:<\/p>\n<p>\u043e\u0442\u043d\u043e\u0441\u0438\u0442\u0435\u043b\u044c\u043d\u043e , \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c, \u0447\u0442\u043e<\/p>\n<p>\u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443<\/p>\n<p>\u041f\u0440\u0438 \u044d\u0442\u043e\u043c \u0434\u043e\u043b\u0436\u043d\u043e \u0431\u044b\u0442\u044c \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435<\/p>\n<p>\u0417\u0430\u043f\u0443\u0441\u0442\u0438\u043c \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u0434\u043b\u044f \u043d\u0430\u0448\u0435\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u0440\u0430.<\/p>\n<details class=\"spoiler\">\n<summary>\u041a\u043e\u0434 \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0439<\/summary>\n<div class=\"spoiler__content\">\n<pre><code class=\"matlab\"># \u043e\u0446\u0435\u043d\u043a\u0438 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 J_upper = [2, 1; 2, 1]; J_lower = [0, 1; 0, 1]; Q1 = [J_upper(1, 1), J_lower(1, 2); J_lower(2, 1), J_upper(2, 2)]; Q2 = [J_lower(1, 1), J_upper(1, 2); J_upper(2, 1), J_lower(2, 2)];  # \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0434\u0435\u0442 \u0432\u043b\u0435\u0432\u043e-\u0432\u0432\u0435\u0440\u0445 disp(\"Algorithm 1\") num_iter = 30; x = x_init; for i = 1:num_iter   x -= Q1 ^ -1 * [F1(x(1), x(2)); F2(x(1), x(2))] endfor  # \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u0438\u0434\u0435\u0442 \u0432\u043f\u0440\u0430\u0432\u043e-\u0432\u043d\u0438\u0437 disp(\"Algorithm 2\") x = x_init; for i = 1:num_iter   x -= Q2 ^ -1 * [F1(x(1), x(2)); F2(x(1), x(2))] endfor<\/code><\/pre>\n<\/p>\n<\/div>\n<\/details>\n<p>\u041f\u043e\u043b\u0443\u0447\u0438\u043c \u0432 \u043e\u0434\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043a\u043e\u0440\u0435\u043d\u044c , \u0432 \u0434\u0440\u0443\u0433\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043a\u043e\u0440\u0435\u043d\u044c  \u0437\u0430 30 \u0438\u0442\u0435\u0440\u0430\u0446\u0438\u0439.<\/p>\n<p>\u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043f\u0440\u0435\u0434\u043b\u043e\u0436\u0435\u043d\u043d\u044b\u0439 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u0435\u0442 \u0438\u0437\u0431\u0430\u0432\u0438\u0442\u044c\u0441\u044f \u043e\u0442 \u043c\u043d\u043e\u0433\u043e\u043a\u0440\u0430\u0442\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u0441\u0440\u0430\u0432\u043d\u0438\u0442\u0435\u043b\u044c\u043d\u043e \u0442\u0440\u0443\u0434\u043e\u0435\u043c\u043a\u043e\u0433\u043e \u043e\u0434\u043d\u043e\u043c\u0435\u0440\u043d\u043e\u0433\u043e \u043c\u0435\u0442\u043e\u0434\u0430 \u0431\u0438\u0441\u0435\u043a\u0446\u0438\u0438 \u0432 \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0435 &#171;\u043b\u0435\u0441\u0435\u043d\u043a\u0430&#187;.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><!----><!----><\/div>\n<p><!----><!----><br \/> \u0441\u0441\u044b\u043b\u043a\u0430 \u043d\u0430 \u043e\u0440\u0438\u0433\u0438\u043d\u0430\u043b \u0441\u0442\u0430\u0442\u044c\u0438 <a href=\"https:\/\/habr.com\/ru\/articles\/787454\/\"> https:\/\/habr.com\/ru\/articles\/787454\/<\/a><br \/><\/br><\/br><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-365735","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/365735","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=365735"}],"version-history":[{"count":0,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=\/wp\/v2\/posts\/365735\/revisions"}],"wp:attachment":[{"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=365735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=365735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/savepearlharbor.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=365735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}