{"id":285,"date":"2021-04-12T09:19:44","date_gmt":"2021-04-12T01:19:44","guid":{"rendered":"http:\/\/www.wayln.com\/?p=285"},"modified":"2021-04-15T09:58:22","modified_gmt":"2021-04-15T01:58:22","slug":"2-5-%e7%9f%a9%e9%98%b5%e5%9b%a0%e5%bc%8f%e5%88%86%e8%a7%a3","status":"publish","type":"post","link":"http:\/\/www.wayln.com\/?p=285","title":{"rendered":"2.5 \u77e9\u9635\u56e0\u5f0f\u5206\u89e3"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#LU\"><span class=\"toc_number toc_depth_1\">1<\/span> LU\u5206\u89e3<\/a><\/li><li><a href=\"#LU-2\"><span class=\"toc_number toc_depth_1\">2<\/span> LU\u5206\u89e3\u7b97\u6cd5<\/a><\/li><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">3<\/span> \u7535\u5b50\u5de5\u7a0b\u4e2d\u7684\u77e9\u9635\u56e0\u5f0f\u5206\u89e3<\/a><\/li><\/ul><\/div>\n<p>\u77e9\u9635A\u7684<strong>\u56e0\u5f0f\u5206\u89e3<\/strong>\u662f\u628aA\u8868\u793a\u4e3a\u4e24\u4e2a\u6216\u66f4\u591a\u4e2a\u77e9\u9635\u7684\u4e58\u79ef\uff0c\u77e9\u9635\u4e58\u6cd5\u662f\u6570\u636e\u7684<strong>\u7efc\u5408<\/strong>\uff08\u628a\u4e24\u4e2a\u6216\u66f4\u591a\u4e2a\u7ebf\u6027\u53d8\u6362\u7684\u4f5c\u7528\u7ed3\u5408\u6210\u4e00\u4e2a\u77e9\u9635\uff09,\u77e9\u9635\u56e0\u5f0f\u5206\u89e3\u662f\u6570\u636e\u7684\u5206\u89e3\uff0c\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u7684\u8bed\u8a00\u90e8\u5206\uff0c\u5c06A\u8868\u793a\u4e3a\u77e9\u9635\u7684\u4e58\u79ef\u662f\u5bf9A\u4e2d\u6570\u636e\u7684\u9884\u5904\u7406\uff0c\u628a\u8fd9\u4e9b\u6570\u636e\u7ec4\u6210\u4e24\u4e2a\u6216\u66f4\u591a\u90e8\u5206\uff0c\u8fd9\u79cd\u7ed3\u6784\u53ef\u80fd\u66f4\u6709\u7528\uff0c\u6216\u8005\u66f4\u4fbf\u4e8e\u8ba1\u7b97\u3002<br \/>\n\u77e9\u9635\u7684\u56e0\u5f0f\u5206\u89e3\uff0c\u4ee5\u53ca\u4ee5\u540e\u7684\u7ebf\u6027\u53d8\u6362\u7684\u5206\u89e3\u5c06\u5728\u8bb8\u591a\u5173\u952e\u5730\u65b9\u51fa\u73b0\u3002<\/p>\n<h2><span id=\"LU\">LU\u5206\u89e3<\/span><\/h2>\n<p>\u8bbeA\u662fmxn\u77e9\u9635\u53ef\u4ee5\u884c\u5316\u7b80\u4e3a\u9636\u68af\u5f62\u800c\u4e0d\u5fc5\u884c\u5bf9\u6362\uff08\u6b64\u540e\uff0c\u6211\u4eec\u5c06\u5904\u7406\u4e00\u822c\u60c5\u5f62\uff09\uff0c\u5219A\u53ef\u5199\u6210\u5f62\u5f0f<span class=\"katex math inline\">A=LU<\/span>,L\u662fmxm\u4e0b\u4e09\u89d2\u77e9\u9635\uff0c\u4e3b\u5bf9\u89d2\u7ebf\u5143\u7d20\u5168\u662f1\uff0cU\u662fA\u7684\u4e00\u4e2a\u7b49\u4ef7\u7684mxn\u9636\u68af\u5f62\u77e9\u9635.\u89c1\u4e0b\u56fe\uff0c\u8fd9\u6837\u4e00\u4e2a\u5206\u89e3\u79f0\u4e3a<strong>LU\u5206\u89e3<\/strong>\uff0c\u77e9\u9635L\u662f\u53ef\u9006\u7684\uff0c\u79f0\u4e3a<strong>\u5355\u4f4d<\/strong>\u4e0b\u4e09\u89d2\u77e9\u9635<\/p>\n<div class=\"katex math multi-line no-emojify\">A=<br \/>\n\\begin{bmatrix}<br \/>\n1&amp;0&amp;0&amp;0\\\\<br \/>\n\\ast&amp;1&amp;0&amp;0\\\\<br \/>\n\\ast&amp;\\ast&amp;1&amp;0\\\\<br \/>\n\\ast&amp;\\ast&amp;\\ast&amp;1<br \/>\n\\end{bmatrix}<br \/>\n\\begin{bmatrix}<br \/>\n\\blacksquare&amp;\\ast&amp;\\ast&amp;\\ast&amp;\\ast\\\\<br \/>\n0&amp;\\blacksquare&amp;\\ast&amp;\\ast&amp;\\ast\\\\<br \/>\n0&amp;0&amp;0&amp;\\blacksquare&amp;\\ast\\\\<br \/>\n0&amp;0&amp;0&amp;0&amp;0<br \/>\n\\end{bmatrix}\n<\/div>\n<p>\u5728\u7814\u7a76\u5982\u4f55\u6784\u9020L\u548cU\u4e4b\u524d\uff0c\u6211\u4eec\u5c06\u770b\u770b\u4ed6\u4eec\u4e3a\u4ec0\u4e48\u8fd9\u4e48\u6709\u7528\u3002\u5f53<span class=\"katex math inline\">A=LU<\/span>\u65f6\uff0c\u65b9\u7a0b<span class=\"katex math inline\">Ax=b<\/span>\u53ef\u5199\u6210<span class=\"katex math inline\">L(Ux)=b<\/span>\uff0c\u628a<span class=\"katex math inline\">Ux<\/span>\u5199\u6210y\uff0c\u53ef\u4ee5\u7531\u89e3\u4e0b\u9762\u4e00\u5806\u65b9\u7a0b\u6765\u6c42\u89e3x:<\/p>\n<div class=\"katex math multi-line no-emojify\">Ly=b\n<\/div>\n<div class=\"katex math multi-line no-emojify\">Ux=y\n<\/div>\n<p>\u9996\u5148\u89e3<span class=\"katex math inline\">Ly=b<\/span>,\u7136\u540e\u89e3<span class=\"katex math inline\">Ux=y<\/span>\u6c42\u5f97x,\u6ca1\u4e2a\u65b9\u7a0b\u90fd\u6bd4\u8f83\u5bb9\u6613\u89e3\uff0c\u56e0\u4e3aL\u548cU\u90fd\u662f\u4e09\u89d2\u77e9\u9635\u3002<br \/>\n<a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_e9ff6246c9ffe2dc9885ece684c2c638.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_e9ff6246c9ffe2dc9885ece684c2c638.jpg\" alt=\"\" \/><\/a><\/p>\n<p>LU\u5206\u89e3\u7684\u8ba1\u7b97\u6548\u7387\u4f9d\u8d56\u4e8e\u5982\u4f55\u6c42L\u548cU<\/p>\n<h2><span id=\"LU-2\">LU\u5206\u89e3\u7b97\u6cd5<\/span><\/h2>\n<p>\u3000\u8bbeA\u53ef\u4ee5\u5316\u4e3a\u9636\u68af\u5f62U\u3002\u5316\u7b80\u8fc7\u7a0b\u4e2d\u4ec5\u7528\u884c\u500d\u52a0\u53d8\u6362\uff0c\u5373\u628a\u4e00\u884c\u7684\u500d\u6570\u52a0\u4e8e\u5b83\u4e0b\u9762\u7684\u53e6\u4e00\u884c\u3002\u8fd9\u6837\uff0c\u5b58\u5728\u5355\u4f4d\u4e0b\u4e09\u89d2\u521d\u7b49\u77e9\u9635<span class=\"katex math inline\">E_1,\\dots,E_p<\/span>\u4f7f<\/p>\n<div class=\"katex math multi-line no-emojify\">E_p\\dots E_1A=U \\tag{3}\n<\/div>\n<p>\u4e8e\u662f<\/p>\n<div class=\"katex math multi-line no-emojify\">A=(E_p\\dots E_1)^{-1}U=LU\n<\/div>\n<p>\u5176\u4e2d<\/p>\n<div class=\"katex math multi-line no-emojify\">L=(E_p\\dots E_1)^{-1} \\tag{4}\n<\/div>\n<p>\u53ef\u4ee5\u8bc1\u660e\uff0c\u5355\u4f4d\u4e0b\u4e09\u89d2\u77e9\u9635\u7684\u9006\u4e5f\u662f\u5355\u4f4d\u4e0b\u4e09\u89d2\u77e9\u9635\uff0c\u4e8e\u662fL\u662f\u5355\u4f4d\u4e0b\u4e09\u89d2\u77e9\u9635<br \/>\n\u6ce8\u610f\uff083\uff09\u4e2d\u7684\u884c\u53d8\u6362\uff0c\u5b83\u628aA\u5316\u4e3aU\uff0c\u6240\u4ee5\u4e5f\u628a\uff084\uff09\u4e2d\u7684L\u5316\u4e3aI\uff0c\u56e0<\/p>\n<div class=\"katex math multi-line no-emojify\">E_p\\dots E_1L-(E_p\\dots E_1)(E_p\\dots E_1)^{-1}=I\n<\/div>\n<p>\u8fd9\u4e00\u70b9\u662f\u6784\u9020L\u7684\u5173\u952e\u3002<\/p>\n<blockquote><p>\n  <strong>LU\u5206\u89e3\u7684\u7b97\u6cd5<\/strong><br \/>\n  1. \u5982\u679c\u53ef\u80fd\u7684\u8bdd\uff0c\u7528\u4e00\u4e9b\u5217\u7684\u500d\u52a0\u53d8\u6362\u628aA\u5316\u4e3a\u9636\u68af\u5f62<br \/>\n  2. \u586b\u5145L\u7684\u5143\u7d20\u4f7f\u76f8\u540c\u7684\u884c\u53d8\u6362\u628aL\u53d8\u4e3aI\n<\/p><\/blockquote>\n<h2><span id=\"i\">\u7535\u5b50\u5de5\u7a0b\u4e2d\u7684\u77e9\u9635\u56e0\u5f0f\u5206\u89e3<\/span><\/h2>\n<p>\u4e0b\u56fe\u4e2d\u7684\u65b9\u6846\u8868\u793a\u67d0\u79cd\u7535\u8def\uff0c\u5177\u6709\u8f93\u5165\u4e0e\u8f93\u51fa\u3002\u7528<span class=\"katex math inline\">\\begin{bmatrix}v_1&#92;\\i_1\\end{bmatrix}<\/span>\u8868\u793a\u8f93\u5165\u7535\u538b\u4e0e\u7535\u6d41\uff08\u7535\u538b\u4ee5\u4f0f\u7279\u4e3a\u5355\u4f4d\uff0c\u7535\u6d41\u7528\u5b89\u57f9\u4e3a\u5355\u4f4d\uff09\uff0c\u8f93\u5165\u51fa\u7535\u538b\u4e0e\u7535\u6d41\u4e3a<span class=\"katex math inline\">\\begin{bmatrix}v_2&#92;\\i_2\\end{bmatrix}<\/span>,\u901a\u5e38\uff0c\u53d8\u6362<span class=\"katex math inline\">\\begin{bmatrix}v_1&#92;\\i_1\\end{bmatrix} \\mapsto \\begin{bmatrix}v_2&#92;\\i_2\\end{bmatrix}<\/span>\u4e3a\u7ebf\u6027\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5b58\u5728\u77e9\u9635A\uff0c\u6210\u4e3a<strong>\u4f20\u9012\u77e9\u9635<\/strong>\uff0c\u4f7f<\/p>\n<div class=\"katex math multi-line no-emojify\">\\begin{bmatrix}<br \/>\nv_2\\\\<br \/>\ni_2<br \/>\n\\end{bmatrix}=<br \/>\nA\\begin{bmatrix}<br \/>\nv_1\\\\<br \/>\ni_1\\\\<br \/>\n\\end{bmatrix}\n<\/div>\n<p><a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_ab66eb2963e0889b7f1f35cfbb867575.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_ab66eb2963e0889b7f1f35cfbb867575.jpg\" alt=\"\" \/><\/a><\/p>\n<p>\u4e0b\u56fe\u8868\u793a\u68af\u7ea7\u7f51\u7edc\uff0c\u4ed6\u6709\u4e24\u4e2a\u56de\u8def\uff08\u4e5f\u53ef\u4ee5\u66f4\u591a\uff09\uff0c\u4ed6\u4eec\u4e32\u8054\u8d77\u6765\uff0c\u6240\u4ee5\u7b2c\u4e00\u4e2a\u7535\u8def\u7684\u8f93\u51fa\u662f\u7b2c\u4e8c\u4e2a\u7535\u8def\u7684\u8f93\u5165\u3002\u5de6\u8fb9\u7684\u7535\u8def\u79f0\u4e3a<strong>\u4e32\u8054\u7535\u8def<\/strong>\uff0c\u5177\u6709\u7535\u963b<span class=\"katex math inline\">R_1<\/span>\uff08\u5355\u4f4d\u4e3a\u6b27\u59c6\uff09\uff0c\u6709\u7aef\u7684\u7535\u8def\u79f0\u4e3a<strong>\u5e76\u8054\u7535\u8def<\/strong>\uff0c\u6709\u7535\u963b<span class=\"katex math inline\">R_2<\/span>\uff0c\u5e94\u7528\u6b27\u59c6\u5b9a\u5f8b\uff0c\u53ef\u4ee5\u8bc1\u660e\u4e32\u8054\u7535\u8def\u4e0e\u5e76\u8054\u7535\u8def\u7684\u4f20\u9012\u77e9\u9635\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\left[\\begin{array}{rr}<br \/>\n1&amp;-R_1\\\\<br \/>\n0&amp;1<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\u4e32\u8054\u7535\u8def\u7684\u4f20\u9012\u77e9\u9635\n<\/div>\n<div class=\"katex math multi-line no-emojify\">\\left[\\begin{array}{rr}<br \/>\n1&amp;0\\\\<br \/>\n-\\frac{1}{R_2}&amp;1<br \/>\n\\end{array}<br \/>\n\\right]<br \/>\n\u5e76\u8054\u7535\u8def\u7684\u4f20\u9012\u77e9\u9635\n<\/div>\n<p><a class=\"wp-editor-md-post-content-link\" href=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_7476318e3bed8b6f32b08ca4deae4335.jpg\"><img decoding=\"async\" src=\"http:\/\/www.wayln.com\/wp-content\/uploads\/2021\/04\/wp_editor_md_7476318e3bed8b6f32b08ca4deae4335.jpg\" alt=\"\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 LU\u5206\u89e32 LU\u5206\u89e3\u7b97\u6cd53 \u7535\u5b50\u5de5\u7a0b\u4e2d\u7684\u77e9\u9635\u56e0\u5f0f\u5206\u89e3 \u77e9\u9635A\u7684\u56e0\u5f0f\u5206\u89e3\u662f\u628aA\u8868\u793a\u4e3a\u4e24\u4e2a\u6216\u66f4 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":338,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21,22,26],"tags":[],"class_list":["post-285","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-21","category-22","category-26"],"_links":{"self":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/285","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=285"}],"version-history":[{"count":5,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/285\/revisions"}],"predecessor-version":[{"id":299,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/285\/revisions\/299"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/media\/338"}],"wp:attachment":[{"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=285"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}