{"id":199746,"date":"2024-05-10T01:16:04","date_gmt":"2024-05-09T17:16:04","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/199746.html"},"modified":"2024-05-10T01:16:08","modified_gmt":"2024-05-09T17:16:08","slug":"matlab-qr%e5%88%86%e8%a7%a3%e7%94%a8%e4%bb%80%e4%b9%88%e7%ae%97%e6%b3%95%e5%ae%9e%e7%8e%b0%e7%9a%84","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/199746.html","title":{"rendered":"matlab QR\u5206\u89e3\u7528\u4ec0\u4e48\u7b97\u6cd5\u5b9e\u73b0\u7684"},"content":{"rendered":"

\"matlab<\/p>\n

\u5728MATLAB\u4e2d\uff0cQR\u5206\u89e3\u901a\u5e38\u662f\u7528Householder\u53d8\u6362<\/strong>\u3001Givens\u65cb\u8f6c<\/strong>\u548cMGS\uff08Modified Gram-Schmidt\uff09\u8fc7\u7a0b<\/strong>\u5b9e\u73b0\u7684\u3002Householder\u53d8\u6362<\/strong>\u662f\u6700\u5e38\u89c1\u548c\u901a\u7528\u7684\u65b9\u6cd5\uff0c\u4e3a\u4e86\u4fdd\u8bc1\u6570\u503c\u7a33\u5b9a\u6027\u548c\u9ad8\u6548\u7684\u5904\u7406\u80fd\u529b\uff0cMATLAB\u4e3b\u8981\u91c7\u7528\u6b64\u7b97\u6cd5\u8fdb\u884cQR\u5206\u89e3\u3002\u8fd9\u79cd\u7b97\u6cd5\u901a\u8fc7\u4e00\u7cfb\u5217\u7684\u6b63\u4ea4\u53d8\u6362\u5c06\u77e9\u9635\u8f6c\u6362\u4e3a\u4e0a\u4e09\u89d2\u77e9\u9635\uff0c\u4ece\u800c\u5b8c\u6210QR\u5206\u89e3\u3002<\/p>\n<\/p>\n

Householder\u53d8\u6362<\/strong>\u7684\u6838\u5fc3\u601d\u60f3\u5728\u4e8e\u901a\u8fc7\u6784\u9020Householder\u77e9\u9635\uff08\u4e00\u79cd\u5177\u6709\u7279\u5b9a\u6027\u8d28\u7684\u6b63\u4ea4\u77e9\u9635\uff09\uff0c\u5c06\u539f\u77e9\u9635\u7684\u67d0\u4e00\u5217\uff08\u6216\u51e0\u5217\uff09\u901a\u8fc7\u6b63\u4ea4\u53d8\u6362\u53d8\u4e3a\u53ea\u6709\u7b2c\u4e00\u4e2a\u5143\u7d20\u975e\u96f6\u7684\u5411\u91cf\uff0c\u4ece\u800c\u9010\u6b65\u5c06\u539f\u77e9\u9635\u8f6c\u5316\u4e3a\u4e0a\u4e09\u89d2\u5f62\u72b6\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u4f18\u70b9\u5305\u62ec\u9ad8\u6548\u6027\u548c\u7a33\u5b9a\u6027\uff0c\u7279\u522b\u662f\u5728\u5904\u7406\u5927\u578b\u77e9\u9635\u65f6\uff0c\u5177\u6709\u660e\u663e\u7684\u901f\u5ea6\u548c\u7cbe\u5ea6\u4f18\u52bf\u3002<\/p>\n<\/p>\n

\u4e00\u3001HOUSEHOLDER \u53d8\u6362\u539f\u7406<\/h3>\n<\/p>\n

Householder\u53d8\u6362\u901a\u8fc7\u6784\u9020\u7279\u5b9a\u7684Householder\u77e9\u9635\u6765\u5b9e\u73b0\u5bf9\u539f\u77e9\u9635\u7684\u8f6c\u6362\u3002Householder\u77e9\u9635\u5f62\u5f0f\u4e3a (H = I – 2vv^T)\uff0c\u5176\u4e2d(v)\u662f\u5355\u4f4d\u5411\u91cf\u3002\u8fd9\u79cd\u53d8\u6362\u7684\u76ee\u7684\u662f\u5c06\u539f\u77e9\u9635\u7684\u7279\u5b9a\u5217\u8f6c\u6362\u4e3a\u4ec5\u5728\u7b2c\u4e00\u4e2a\u4f4d\u7f6e\u6709\u975e\u96f6\u5143\u7d20\u7684\u5f62\u5f0f\uff0c\u5176\u4ed6\u4f4d\u7f6e\u4e3a\u96f6\u3002Householder\u53d8\u6362\u662f\u5bf9\u79f0\u548c\u6b63\u4ea4\u7684\uff0c\u56e0\u6b64\u4fdd\u6301\u4e86\u539f\u77e9\u9635\u7684\u8bb8\u591a\u6570\u5b66\u6027\u8d28\u4e0d\u53d8\uff0c\u7279\u522b\u662f\u6b63\u4ea4\u6027\u8d28\u4fdd\u8bc1\u4e86\u8ba1\u7b97\u8fc7\u7a0b\u7684\u6570\u503c\u7a33\u5b9a\u6027\u3002<\/p>\n<\/p>\n

\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u901a\u8fc7\u9010\u5217\u6784\u9020Householder\u77e9\u9635\u5e76\u5de6\u4e58\u539f\u77e9\u9635\uff0c\u53ef\u4ee5\u9010\u6b65\u5c06\u539f\u77e9\u9635\u8f6c\u6362\u4e3a\u4e0a\u4e09\u89d2\u77e9\u9635\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u6b21\u53d8\u6362\u53ea\u5f71\u54cd\u5f53\u524d\u5904\u7406\u5217\u53ca\u5176\u540e\u9762\u7684\u5217\uff0c\u4fdd\u8bc1\u4e86\u7b97\u6cd5\u7684\u9ad8\u6548\u6027\u3002<\/p>\n<\/p>\n

\u4e8c\u3001GIVENS\u65cb\u8f6c\u539f\u7406<\/h3>\n<\/p>\n

Givens\u65cb\u8f6c\u662f\u53e6\u4e00\u79cd\u7528\u4e8eQR\u5206\u89e3\u7684\u65b9\u6cd5\uff0c\u5b83\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c\u5c06\u77e9\u9635\u7684\u7279\u5b9a\u5143\u7d20\u53d8\u4e3a\u96f6\u3002\u76f8\u6bd4Householder\u53d8\u6362\uff0cGivens\u65cb\u8f6c\u66f4\u52a0\u7075\u6d3b\uff0c\u9002\u7528\u4e8e\u7a00\u758f\u77e9\u9635\u7684\u5904\u7406\u3002Givens\u65cb\u8f6c\u901a\u8fc7\u6784\u9020\u4e00\u4e2a\u65cb\u8f6c\u77e9\u9635\u6765\u5b9e\u73b0\u67d0\u4e24\u884c\u7684\u65cb\u8f6c\uff0c\u4ece\u800c\u8ba9\u77e9\u9635\u7684\u7279\u5b9a\u4f4d\u7f6e\u4e0a\u7684\u5143\u7d20\u53d8\u4e3a0\u3002<\/p>\n<\/p>\n

Givens\u65cb\u8f6c\u7684\u4e3b\u8981\u4f18\u70b9\u662f\u5b83\u80fd\u591f\u9488\u5bf9\u77e9\u9635\u7684\u7279\u5b9a\u5143\u7d20\u8fdb\u884c\u64cd\u4f5c\uff0c\u7279\u522b\u662f\u5728\u5904\u7406\u542b\u6709\u96f6\u5143\u7d20\u7684\u7a00\u758f\u77e9\u9635\u65f6\uff0c\u53ef\u4ee5\u6709\u6548\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u8ba1\u7b97\uff0c\u63d0\u9ad8\u7b97\u6cd5\u6548\u7387\u3002\u7136\u800c\uff0cGivens\u65cb\u8f6c\u6d89\u53ca\u7684\u65cb\u8f6c\u64cd\u4f5c\u76f8\u6bd4Householder\u53d8\u6362\u66f4\u52a0\u590d\u6742\uff0c\u4f1a\u5bfc\u81f4\u8ba1\u7b97\u91cf\u7565\u6709\u589e\u52a0\u3002<\/p>\n<\/p>\n

\u4e09\u3001MODIFIED GRAM-SCHMIDT \u8fc7\u7a0b<\/h3>\n<\/p>\n

Modified Gram-Schmidt\u8fc7\u7a0b\uff08MGS\uff09\u662fGram-Schmidt\u6b63\u4ea4\u5316\u8fc7\u7a0b\u7684\u4e00\u79cd\u6539\u8fdb\u5f62\u5f0f\uff0c\u7528\u4e8e\u751f\u6210\u6b63\u4ea4\u6216\u6807\u51c6\u6b63\u4ea4\u5411\u91cf\u7ec4\uff0c\u4ece\u800c\u5b9e\u73b0QR\u5206\u89e3\u3002MGS\u8fc7\u7a0b\u76f8\u6bd4\u4f20\u7edf\u7684Gram-Schmidt\u8fc7\u7a0b\u6709\u66f4\u597d\u7684\u6570\u503c\u7a33\u5b9a\u6027\u3002<\/p>\n<\/p>\n

\u5728MGS\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u4e00\u6b65\u7684\u6b63\u4ea4\u5316\u8fc7\u7a0b\u90fd\u662f\u57fa\u4e8e\u5df2\u7ecf\u88ab\u6b63\u4ea4\u5316\u7684\u5411\u91cf\u6765\u5b8c\u6210\u7684\uff0c\u8fd9\u610f\u5473\u7740\u6bcf\u6b21\u8ba1\u7b97\u90fd\u4f1a\u4fee\u6b63\u7531\u4e8e\u8ba1\u7b97\u8bef\u5dee\u5bfc\u81f4\u7684\u6b63\u4ea4\u6027\u4e27\u5931\uff0c\u4ece\u800c\u4fdd\u8bc1\u4e86\u6574\u4e2a\u8fc7\u7a0b\u7684\u7a33\u5b9a\u6027\u3002MGS\u8fc7\u7a0b\u867d\u7136\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u4e0d\u5982Householder\u53d8\u6362\u6548\u7387\u9ad8\uff0c\u4f46\u5176\u7b80\u5355\u76f4\u89c2\uff0c\u6613\u4e8e\u5b9e\u73b0\uff0c\u4e14\u5728\u5904\u7406\u67d0\u4e9b\u7279\u5b9a\u7c7b\u578b\u7684\u77e9\u9635\u65f6\u4ecd\u7136\u5177\u6709\u4f18\u52bf\u3002<\/p>\n<\/p>\n

\u56db\u3001MATLAB\u4e2d\u7684QR\u5206\u89e3\u5b9e\u73b0<\/h3>\n<\/p>\n

\u5728MATLAB\u4e2d\uff0cQR\u5206\u89e3\u4e00\u822c\u901a\u8fc7qr<\/code>\u51fd\u6570\u6765\u5b9e\u73b0\u3002\u8be5\u51fd\u6570\u5185\u90e8\u6839\u636e\u77e9\u9635\u7684\u7c7b\u578b\u548c\u7ed3\u6784\u81ea\u52a8\u9009\u62e9\u6700\u5408\u9002\u7684\u7b97\u6cd5\uff08\u4e3b\u8981\u662fHouseholder\u53d8\u6362\uff09\u3002\u5bf9\u4e8e\u7528\u6237\u800c\u8a00\uff0c\u53ea\u9700\u8981\u63d0\u4f9b\u5f85\u5206\u89e3\u7684\u77e9\u9635\u5373\u53ef\u83b7\u5f97QR\u5206\u89e3\u7684\u7ed3\u679c\u3002\u5982\u679c\u9700\u8981\u66f4\u52a0\u8be6\u7ec6\u5730\u63a7\u5236\u5206\u89e3\u8fc7\u7a0b\uff0cMATLAB\u4e5f\u63d0\u4f9b\u4e86\u9009\u9879\uff0c\u5141\u8bb8\u7528\u6237\u6307\u5b9a\u4f7f\u7528\u67d0\u79cd\u7279\u5b9a\u7684\u7b97\u6cd5\uff08\u5982Givens\u65cb\u8f6c\u6216MGS\u8fc7\u7a0b\uff09\u6765\u5b8c\u6210\u5206\u89e3\u3002<\/p>\n<\/p>\n

\u901a\u8fc7qr<\/code>\u51fd\u6570\uff0c\u7528\u6237\u4e0d\u4ec5\u53ef\u4ee5\u83b7\u53d6QR\u5206\u89e3\u7ed3\u679c\uff0c\u8fd8\u53ef\u4ee5\u8fdb\u4e00\u6b65\u5e94\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3001\u8ba1\u7b97\u77e9\u9635\u7684\u9006\u4ee5\u53ca\u6267\u884c\u5176\u4ed6\u7ebf\u6027\u4ee3\u6570\u64cd\u4f5c\u3002MATLAB\u7684\u8fd9\u79cd\u8bbe\u8ba1\u5927\u5927\u7b80\u5316\u4e86QR\u5206\u89e3\u7684\u4f7f\u7528\uff0c\u4f7f\u5176\u6210\u4e3a\u5904\u7406\u7ebf\u6027\u4ee3\u6570\u95ee\u9898\u7684\u5f3a\u5927\u5de5\u5177\u3002<\/p>\n<\/p>\n

\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

1. QR\u5206\u89e3\u5728Matlab\u4e2d\u662f\u901a\u8fc7\u54ea\u79cd\u7b97\u6cd5\u6765\u5b9e\u73b0\u7684\uff1f<\/strong>
\nMatlab\u4e2d\u7684QR\u5206\u89e3\u7b97\u6cd5\u91c7\u7528\u4e86Householder\u53d8\u6362\u548cGivens\u65cb\u8f6c\u4e24\u79cd\u7b97\u6cd5\u7684\u6df7\u5408\u5b9e\u73b0\u3002\u5176\u4e2d\uff0cHouseholder\u53d8\u6362\u4e3b\u8981\u7528\u4e8e\u5904\u7406\u5217\u5411\u91cf\u7684\u6b63\u4ea4\u53d8\u6362\uff0c\u800cGivens\u65cb\u8f6c\u5219\u4e3b\u8981\u7528\u4e8e\u5904\u7406\u4e0a\u4e09\u89d2\u77e9\u9635\u7684\u53d8\u6362\u3002\u8fd9\u4e24\u79cd\u7b97\u6cd5\u7684\u7ed3\u5408\u80fd\u591f\u9ad8\u6548\u5730\u8fdb\u884cQR\u5206\u89e3\uff0c\u63d0\u9ad8\u4e86\u7b97\u6cd5\u7684\u8ba1\u7b97\u6548\u7387\u548c\u7a33\u5b9a\u6027\u3002<\/p>\n

2. QR\u5206\u89e3\u7b97\u6cd5\u5728Matlab\u4e2d\u7684\u5e94\u7528\u6709\u54ea\u4e9b\uff1f<\/strong>
\n\u5728Matlab\u4e2d\uff0cQR\u5206\u89e3\u7b97\u6cd5\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6c42\u89e3\u7ebf\u6027\u65b9\u7a0b\u7ec4\u3001\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u3001\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u8ba1\u7b97\u7b49\u6570\u503c\u8ba1\u7b97\u4efb\u52a1\u3002QR\u5206\u89e3\u80fd\u591f\u5c06\u4e00\u4e2a\u77e9\u9635\u5206\u89e3\u4e3a\u4e00\u4e2a\u6b63\u4ea4\u77e9\u9635\u548c\u4e00\u4e2a\u4e0a\u4e09\u89d2\u77e9\u9635\u7684\u4e58\u79ef\uff0c\u4ece\u800c\u65b9\u4fbf\u4e86\u5bf9\u77e9\u9635\u7684\u5404\u79cd\u8ba1\u7b97\u548c\u5206\u6790\u3002<\/p>\n

3. QR\u5206\u89e3\u5728Matlab\u4e2d\u7684\u7b97\u6cd5\u5b9e\u73b0\u6709\u4f55\u7279\u70b9\uff1f<\/strong>
\nMatlab\u4e2d\u7684QR\u5206\u89e3\u7b97\u6cd5\u5177\u6709\u9ad8\u5ea6\u7684\u53ef\u5b9a\u5236\u6027\u548c\u9002\u5e94\u6027\u3002Matlab\u63d0\u4f9b\u4e86\u591a\u79cdQR\u5206\u89e3\u7684\u51fd\u6570\uff0c\u5982qr<\/code>\u3001qrdelete<\/code>\u3001qrinsert<\/code>\u7b49\uff0c\u53ef\u4ee5\u6839\u636e\u5177\u4f53\u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u51fd\u6570\u8fdb\u884c\u5206\u89e3\u3002\u53e6\u5916\uff0cMatlab\u8fd8\u652f\u6301\u5e76\u884c\u8ba1\u7b97\u548c\u4f18\u5316\u7684QR\u5206\u89e3\u7b97\u6cd5\uff0c\u80fd\u591f\u5145\u5206\u5229\u7528\u591a\u6838\u5904\u7406\u5668\u548c\u77e2\u91cf\u6307\u4ee4\u96c6\uff0c\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002\u901a\u8fc7\u8c03\u6574\u7b97\u6cd5\u7684\u53c2\u6570\u548c\u9009\u9879\uff0c\u8fd8\u53ef\u4ee5\u8fdb\u4e00\u6b65\u4f18\u5316\u7b97\u6cd5\u7684\u7a33\u5b9a\u6027\u548c\u7cbe\u5ea6\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728MATLAB\u4e2d\uff0cQR\u5206\u89e3\u901a\u5e38\u662f\u7528Householder\u53d8\u6362\u3001Givens\u65cb\u8f6c\u548cMGS\uff08Modified Gr […]","protected":false},"author":3,"featured_media":199747,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/199746"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=199746"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/199746\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/199747"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=199746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=199746"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=199746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}