{"id":589,"date":"2021-05-24T20:14:20","date_gmt":"2021-05-24T12:14:20","guid":{"rendered":"http:\/\/www.wayln.com\/?p=589"},"modified":"2021-09-11T18:08:56","modified_gmt":"2021-09-11T10:08:56","slug":"5-6-%e7%a6%bb%e6%95%a3%e5%8a%a8%e5%8a%9b%e7%b3%bb%e7%bb%9f","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=589","title":{"rendered":"5.6 \u79bb\u6563\u52a8\u529b\u7cfb\u7edf"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">1<\/span> \u6355\u98df\u8005-\u98df\u9975\u7cfb\u7edf<\/a><\/li><li><a href=\"#i-2\"><span class=\"toc_number toc_depth_1\">2<\/span> \u89e3\u7684\u51e0\u4f55\u610f\u4e49<\/a><\/li><li><a href=\"#i-3\"><span class=\"toc_number toc_depth_1\">3<\/span> \u53d8\u91cf\u4ee3\u6362<\/a><\/li><li><a href=\"#i-4\"><span class=\"toc_number toc_depth_1\">4<\/span> \u590d\u7279\u5f81\u503c<\/a><\/li><li><a href=\"#i-5\"><span class=\"toc_number toc_depth_1\">5<\/span> \u534a\u70b9\u732b\u5934\u9e70\u7684\u751f\u5b58<\/a><\/li><\/ul><\/div>\n<p>\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u63d0\u4f9b\u4e86\u7ebf\u7d22\uff0c\u4f7f\u6211\u4eec\u7406\u89e3\u7531\u5dee\u5206\u65b9\u7a0b<span class=\"katex math inline\">x_{k+1}=Ax_{k}<\/span>\u63cf\u8ff0\u7684\u52a8\u529b\u7cfb\u7edf\u7684\u957f\u671f\u884c\u4e3a\u6216\u8fdb\u5316\u3002<br \/>\n\u6211\u4eec\u5047\u8bbeA\u53ef\u5bf9\u89d2\u5316\uff0c\u6709n\u4e2a\u7ebf\u6027\u65e0\u5173\u7684\u7279\u5f81\u5411\u91cf<span class=\"katex math inline\">v_1,\\dots,v_n<\/span>\u548c\u5bf9\u5e94\u7684\u7279\u5f81\u503c<span class=\"katex math inline\">\\lambda_1,\\dots,\\lambda_m<\/span>\u3002\u4e3a\u65b9\u4fbf\u8d77\u89c1\uff0c\u5047\u8bbe\u7279\u5f81\u5411\u91cf\u5df2\u6309<span class=\"katex math inline\">|\\lambda_1| \\geqslant|\\lambda_2|\\geqslant\\dots\\geqslant|\\lambda_n|<\/span>\u7684\u987a\u5e8f\u6392\u5217\u597d\uff0c\u56e0\u4e3a<span class=\"katex math inline\">&#92;{v_1,\\dots,v_n&#92;}<\/span>\u662f<span class=\"katex math inline\">R^n<\/span>\u7684\u57fa\uff0c\u6545\u4efb\u4e00\u521d\u59cb\u5411\u91cf<span class=\"katex math inline\">x_0<\/span>\u53ef\u4ee5\u552f\u4e00\u6807\u793a\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">x_0=c_1v_1+\\dots+c_nv_n \\tag{1}\n<\/div>\n<p>x0\u7684\u8fd9\u79cd\u7279\u5f81\u5411\u91cf\u5206\u89e3\u786e\u5b9a\u4e86\u5e8f\u5217<span class=\"katex math inline\">&#92;{x_k&#92;}<\/span>\u6240\u53d1\u751f\u7684\u60c5\u51b5\uff0c\u4e0b\u4e00\u6b65\u8ba1\u7b97\u5c065.2\u8282\u4f8b5\u7684\u7b80\u5355\u60c5\u51b5\u4e00\u822c\u5316\uff0c\u56e0\u4e3a<span class=\"katex math inline\">v_i<\/span>\u662f\u7279\u5f81\u5411\u91cf\uff0c\u6240\u4ee5<\/p>\n<div class=\"katex math multi-line no-emojify\">x_1=Ax_0=c_1Av_1+\\dots+c_nAv_n\\\\=c_1\\lambda_1v_1+\\dots+c_n\\lambda_nv_n\n<\/div>\n<p>\u4e00\u822c\u6709<\/p>\n<div class=\"katex math multi-line no-emojify\">x_k=c_1(\\lambda_1)^kv_1+\\dots+c_n(\\lambda_n)^kv_n(k=0,1,2,\\dots)    \\tag{2}\n<\/div>\n<h1><span id=\"i\">\u6355\u98df\u8005-\u98df\u9975\u7cfb\u7edf<\/span><\/h1>\n<h1><span id=\"i-2\">\u89e3\u7684\u51e0\u4f55\u610f\u4e49<\/span><\/h1>\n<p>\u5f53A\u4e3a2&#215;2\u77e9\u9635\u65f6\uff0c\u53ef\u4ee5\u901a\u8fc7\u7cfb\u7edf\u53d1\u5c55\u8d8b\u52bf\u7684\u51e0\u4f55\u63cf\u8ff0\u6765\u8865\u5145\u89e3\u91ca\u4ee3\u6570\u8ba1\u7b97\u3002\u6211\u4eec\u53ef\u4ee5\u628a\u65b9\u7a0b<span class=\"katex math inline\">x_{k+1}=Ax_k<\/span>\u770b\u505a\u662f<span class=\"katex math inline\">R^2<\/span>\u4e2d\u7684\u521d\u59cb\u70b9<span class=\"katex math inline\">x_0<\/span>\u88ab\u6620\u5c04<span class=\"katex math inline\">x\\mapsto Ax<\/span>\u91cd\u590d\u53d8\u6362\u7684\u63cf\u8ff0\uff0c\u7531<span class=\"katex math inline\">x_0,x_1,\\dots<\/span>\u7ec4\u6210\u7684\u56fe\u5f62\u79f0\u4e3a\u52a8\u529b\u7cfb\u7edf\u7684\u8f68\u8ff9\u3002<\/p>\n<h1><span id=\"i-3\">\u53d8\u91cf\u4ee3\u6362<\/span><\/h1>\n<h1><span id=\"i-4\">\u590d\u7279\u5f81\u503c<\/span><\/h1>\n<h1><span id=\"i-5\">\u534a\u70b9\u732b\u5934\u9e70\u7684\u751f\u5b58<\/span><\/h1>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 \u6355\u98df\u8005-\u98df\u9975\u7cfb\u7edf2 \u89e3\u7684\u51e0\u4f55\u610f\u4e493 \u53d8\u91cf\u4ee3\u63624 \u590d\u7279\u5f81\u503c5 \u534a\u70b9\u732b\u5934\u9e70\u7684\u751f\u5b58 \u7279\u5f81\u503c\u548c\u7279\u5f81 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":410,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-589","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/589","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=589"}],"version-history":[{"count":5,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/589\/revisions"}],"predecessor-version":[{"id":595,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/589\/revisions\/595"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/410"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}