{"id":9004,"date":"2023-10-08T16:21:25","date_gmt":"2023-10-08T08:21:25","guid":{"rendered":"\/?p=9004"},"modified":"2024-01-02T10:28:23","modified_gmt":"2024-01-02T02:28:23","slug":"%e5%90%91%e9%87%8f%e7%9a%84%e8%8c%83%e6%95%b0-%e6%9b%bc%e5%93%88%e9%a1%bf%e8%b7%9d%e7%a6%bb","status":"publish","type":"post","link":"\/?p=9004","title":{"rendered":"\u5411\u91cf\u7684\u8303\u6570-\u66fc\u54c8\u987f\u8ddd\u79bb"},"content":{"rendered":"

\u6570\u5b66\u5b9a\u4e49<\/h2>\n

\u8303\u6570\u7684\u516c\u5f0f\u662f\u5411\u91cf\u6bcf\u4e2a\u5206\u91cf \u7edd\u5bf9\u503c P \u6b21\u65b9 \u6c42\u548c\uff0c \u518d\u7528\u5e42\u51fd\u6570\u8ba1\u7b97 P \u5206\u4e4b\u4e00\uff0c\u8fd9\u91cc P \u80af\u5b9a\u662f\u6574\u6570
\n$$\\sqrt{a^2+b^2}$$
\n(\\sqrt{a^2+b^2})
\n1\uff0c2\uff0c3...\u5230\u6b63\u65e0\u7a77\u90fd\u662f\u53ef\u4ee5\u7684<\/p>\n

\u5411\u91cf\u7684\u8303\u6570\u5c31\u662f\u628a\u5411\u91cf\u53d8\u6210\u4e00\u4e2a\u6807\u91cf\uff0c\u8303\u6570\u7684\u8868\u793a\u5c31\u662f\u4e24\u4e2a\u7ad6\u7ebf\u6765\u8868\u793a\uff0c\u7136\u540e\u53f3\u4e0b\u89d2\u5199\u4e0a P
\n$$||x||p = (\\sum<\/em>{i=1}^{n}|x_i|^p)^\\frac{1}{p}$$<\/p>\n

\"image-20231008155952610\" <\/p>\n

1 \u8303\u6570\u662f\u7edd\u5bf9\u503c\u52a0\u548c\uff0c1 \u8303\u6570\u5199\u6210 L1
\n$$
\n||x||1 = \\sum<\/em>{i=1}^{n}|x_i|
\n$$
\n2 \u8303\u6570\u662f\u5e73\u65b9\u52a0\u548c\u5f00\u6839\u53f7\uff0c\u5176\u5b9e\u4ee3\u8868\u7684\u662f\u5411\u91cf\u7684\u957f\u5ea6\uff0c\u9ad8\u4e2d\u65f6\u5019\u5b66\u7684\u5411\u91cf\u7684\u6a21\uff0c2 \u8303\u6570\u5199\u6210 L2
\n$$
\n||x||2 = \\sqrt{\\sum<\/em>{i=1}^{n}(x_i)^2}
\n$$
\n\u8303\u6570\u5728\u540e\u9762\u662f\u975e\u5e38\u6709\u7528\u7684\uff0c\u5728\u540e\u9762\u8bb2\u6b63\u5219\u9879\u7684\u65f6\u5019\u4f1a\u7528\u5230<\/p>\n

L1\u8303\u6570\u7684\u6b63\u5219\u9879\uff1a$$\\sum_{i=1}^{n}|w_i|$$<\/p>\n

L2\u8303\u6570\u7684\u6b63\u5219\u9879\uff1a$$\\sum_{i=1}^{n}(w_i)^2$$<\/p>\n

\u51e0\u4f55\u610f\u4e49<\/h2>\n

\u8d6b\u5c14\u66fc\u00b7\u95f5\u53ef\u592b\u65af\u57fa\u5728\u5c11\u5e74\u65f6\u671f\u5c31\u5728\u6570\u5b66\u65b9\u9762\u8868\u73b0\u51fa\u6781\u9ad8\u7684\u5929\u5206\uff0c\u4ed6\u662f\u540e\u6765\u56db\u7ef4\u65f6\u7a7a\u7406\u8bba\u7684\u521b\u7acb\u8005\uff0c\u4e5f\u66fe\u7ecf\u662f\u8457\u540d\u7269\u7406\u5b66\u5bb6\u7231\u56e0\u65af\u5766\u7684\u8001\u5e08\u3002<\/p>\n

\u66fc\u54c8\u987f\u8ddd\u79bb\u4e5f\u53eb\u51fa\u79df\u8f66\u8ddd\u79bb\uff0c\u7528\u6765\u6807\u660e\u4e24\u4e2a\u70b9\u5728\u6807\u51c6\u5750\u6807\u7cfb\u4e0a\u7684\u7edd\u5bf9\u8f74\u8ddd\u603b\u548c\u3002\u7b80\u5355\u6765\u8bf4\uff0c\u5bf9\u6bd4\u4e00\u4e0b\u6b27\u6c0f\u8ddd\u79bb\u3002<\/p>\n

\u6b27\u6c0f\u8ddd\u79bb\u91cc\u7684\u8ddd\u79bb\u8ba1\u7b97\uff1a<\/p>\n

\"img\"<\/p>\n

\u66fc\u54c8\u987f\u8ddd\u79bb\u4e2d\u7684\u8ddd\u79bb\u8ba1\u7b97\uff1a<\/p>\n

\"img\"<\/p>\n

\u66fc\u54c8\u987f\u8ddd\u79bb\u4e2d\u7684\u8ddd\u79bb\u8ba1\u7b97\u516c\u5f0f\u6bd4\u6b27\u6c0f\u8ddd\u79bb\u7684\u8ba1\u7b97\u516c\u5f0f\u770b\u8d77\u6765\u7b80\u6d01\u5f88\u591a\uff0c\u53ea\u9700\u8981\u628a\u4e24\u4e2a\u70b9\u5750\u6807\u7684 x \u5750\u6807\u76f8\u51cf\u53d6\u7edd\u5bf9\u503c\uff0cy \u5750\u6807\u76f8\u51cf\u53d6\u7edd\u5bf9\u503c\uff0c\u518d\u52a0\u548c\u3002<\/p>\n

\u4ece\u516c\u5f0f\u5b9a\u4e49\u4e0a\u770b\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u4e00\u5b9a\u662f\u4e00\u4e2a\u975e\u8d1f\u6570\uff0c\u8ddd\u79bb\u6700\u5c0f\u7684\u60c5\u51b5\u5c31\u662f\u4e24\u4e2a\u70b9\u91cd\u5408\uff0c\u8ddd\u79bb\u4e3a 0\uff0c\u8fd9\u4e00\u70b9\u548c\u6b27\u6c0f\u8ddd\u79bb\u4e00\u6837\u3002\u66fc\u54c8\u987f\u8ddd\u79bb\u548c\u6b27\u6c0f\u8ddd\u79bb\u7684\u610f\u4e49\u76f8\u8fd1\uff0c\u4e5f\u662f\u4e3a\u4e86\u63cf\u8ff0\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u4e0d\u540c\u7684\u662f\u66fc\u54c8\u987f\u8ddd\u79bb\u53ea\u9700\u8981\u505a\u52a0\u51cf\u6cd5\uff0c\u8fd9\u4f7f\u5f97\u8ba1\u7b97\u673a\u5728\u5927\u91cf\u7684\u8ba1\u7b97\u8fc7\u7a0b\u4e2d\u4ee3\u4ef7\u66f4\u4f4e\uff0c\u800c\u4e14\u4f1a\u6d88\u9664\u5728\u5f00\u5e73\u65b9\u8fc7\u7a0b\u4e2d\u53d6\u8fd1\u4f3c\u503c\u800c\u5e26\u6765\u7684\u8bef\u5dee\u3002\u4e0d\u4ec5\u5982\u6b64\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u5728\u4eba\u8131\u79bb\u8ba1\u7b97\u673a\u505a\u8ba1\u7b97\u7684\u65f6\u5019\u4e5f\u4f1a\u5f88\u65b9\u4fbf\u3002\u4e3e\u4f8b\u5982\u4e0b\u3002<\/p>\n

\"img\"<\/p>\n

\u5728\u56fd\u9645\u8c61\u68cb\u68cb\u76d8\uff08\u56fe 2\uff09\u4e0a\uff0c\u6709\u8fd9\u79cd\u6a2a\u5e73\u7ad6\u76f4\u7684\u683c\u5b50\uff0c\u63cf\u8ff0\u683c\u5b50\u548c\u683c\u5b50\u4e4b\u95f4\u7684\u8ddd\u79bb\u53ef\u4ee5\u76f4\u63a5\u7528\u66fc\u54c8\u987f\u8ddd\u79bb\u3002\u5982 A1 \u683c\u5b50\u5230 C4 \u683c\u5b50\u7684\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97\u5982\u4e0b\uff1a<\/p>\n

\"img\"<\/p>\n

\u4e24\u4e2a\u683c\u5b50\u4e4b\u95f4\u7684\u66fc\u54c8\u987f\u8ddd\u79bb\u4e3a 5\u3002<\/p>\n

\u4e4b\u6240\u4ee5\u66fc\u54c8\u987f\u8ddd\u79bb\u53c8\u88ab\u79f0\u4e3a\u51fa\u79df\u8f66\u8ddd\u79bb\u662f\u56e0\u4e3a\u5728\u50cf\u7ebd\u7ea6\u66fc\u54c8\u987f\u533a\u8fd9\u6837\u7684\u5730\u533a\u6709\u5f88\u591a\u7531\u6a2a\u5e73\u7ad6\u76f4\u7684\u8857\u9053\u6240\u5207\u6210\u7684\u8857\u533a\uff08Block\uff09\uff0c\u51fa\u79df\u8f66\u53f8\u673a\u8ba1\u7b97\u4ece\u4e00\u4e2a\u4f4d\u7f6e\u5230\u53e6\u4e00\u4e2a\u4f4d\u7f6e\u7684\u8ddd\u79bb\uff0c\u901a\u5e38\u76f4\u63a5\u7528\u8857\u533a\u7684\u4e24\u4e2a\u5750\u6807\u5206\u522b\u76f8\u51cf\uff0c\u518d\u76f8\u52a0\uff0c\u8fd9\u4e2a\u7ed3\u679c\u5c31\u662f\u4ed6\u5373\u5c06\u5f00\u8f66\u901a\u8fc7\u7684\u8857\u533a\u6570\u91cf\uff0c\u800c\u5b8c\u5168\u6ca1\u6709\u5fc5\u8981\u7528\u6b27\u6c0f\u8ddd\u79bb\u6765\u6c42\u89e3\u2014\u2014\u7b97\u8d77\u6765\u8d85\u7ea7\u9ebb\u70e6\u8fd8\u6ca1\u6709\u610f\u4e49\uff0c\u6bd5\u7adf\u8c01\u4e5f\u6ca1\u529e\u6cd5\u4ece\u6b27\u6c0f\u8ddd\u79bb\u7684\u76f4\u7ebf\u4e0a\u98de\u8fc7\u53bb\u3002\u5982\u56fe 3 \u6240\u793a\uff0c\u5047\u8bbe\u4e00\u8f86\u51fa\u79df\u8f66\u8981\u4ece\u4e0a\u9762\u7684\u5706\u5708\u4f4d\u7f6e\u8d70\u5230\u4e0b\u9762\u7684\u5706\u5708\u4f4d\u7f6e\uff0c\u65e0\u8bba\u662f\u5de6\u8fb9\u7684\u7ebf\u8def\uff0c\u8fd8\u662f\u53f3\u8fb9\u7684\u7ebf\u8def\uff0c\u90fd\u8981\u7ecf\u8fc7 11 \u4e2a\u8857\u533a\uff0c\u800c\u8fd9\u4e2a 11 \u5c31\u662f\u66fc\u54c8\u987f\u8ddd\u79bb\u3002<\/p>\n

\u4ece\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u5b9a\u4e49\u5c31\u80fd\u770b\u51fa\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u521b\u7acb\uff0c\u4e0e\u5176\u8bf4\u6709\u5f88\u5927\u7684\u5b66\u672f\u610f\u4e49\u4e0d\u5982\u8bf4\u66f4\u591a\u7684\u662f\u5e94\u7528\u610f\u4e49\u3002\u8fd9\u4e5f\u662f\u672c\u4e66\u4e00\u76f4\u60f3\u8bf4\u7684\u4e00\u70b9\uff0c\u6570\u5b66\u5c31\u5728\u6211\u4eec\u8eab\u8fb9\uff0c\u5b83\u662f\u6211\u4eec\u7684\u5de5\u5177\uff0c\u80fd\u5e2e\u6211\u4eec\u89e3\u51b3\u95ee\u9898\u800c\u4e0d\u662f\u5e26\u6765\u9ebb\u70e6\u3002<\/p>\n

\"img\"<\/p>\n

\u4e0a\u9762\u7684\u516c\u5f0f\u53ea\u7ed9\u4e86\u4e8c\u7ef4\u7a7a\u95f4\u4e0a\u7684\u66fc\u54c8\u987f\u8ddd\u79bb\u516c\u5f0f\uff0c\u4e09\u7ef4\u3001\u56db\u7ef4\u6216\u8005\u66f4\u591a\u7ef4\u5ea6\u7684\u8ba1\u7b97\u539f\u7406\u662f\u4e00\u6837<\/p>\n","protected":false},"excerpt":{"rendered":"

\u6570\u5b66\u5b9a\u4e49 \u8303\u6570\u7684\u516c\u5f0f\u662f\u5411\u91cf\u6bcf\u4e2a\u5206\u91cf \u7edd\u5bf9\u503c P \u6b21\u65b9 \u6c42\u548c\uff0c \u518d\u7528\u5e42\u51fd\u6570\u8ba1\u7b97 P \u5206\u4e4b\u4e00\uff0c\u8fd9\u91cc P \u80af\u5b9a\u662f\u6574\u6570 $$\\sqrt{a^2+ \u2026 …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[213],"tags":[],"_links":{"self":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9004"}],"collection":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9004"}],"version-history":[{"count":5,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9004\/revisions"}],"predecessor-version":[{"id":9066,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9004\/revisions\/9066"}],"wp:attachment":[{"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9004"},{"taxonomy":"post_tag","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}