{"id":190,"date":"2014-12-25T15:26:33","date_gmt":"2014-12-25T07:26:33","guid":{"rendered":"http:\/\/planckscale.info\/?p=190"},"modified":"2015-04-08T12:12:58","modified_gmt":"2015-04-08T04:12:58","slug":"levenberg-marquardt%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/mindspectrum.xyz\/en\/2014\/12\/25\/levenberg-marquardt%e7%ae%97%e6%b3%95\/","title":{"rendered":"Levenberg-Marquardt\u7b97\u6cd5"},"content":{"rendered":"

\u5306\u5306\u4e00\u66f4\u3002\u8fd8\u6ca1\u5199\u5b8c\uff0c\u5bf9\u4e0d\u8d77\u6211\u592a\u61d2\u4e86T_T<\/p>\n

\u7248\u6743\u58f0\u660e\uff1a\u539f\u521b\u4f5c\u54c1\uff0c\u6b22\u8fce\u8f6c\u8f7d\uff0c\u4f46\u8f6c\u8f7d\u8bf7\u4ee5\u8d85\u94fe\u63a5\u5f62\u5f0f\u6ce8\u660e\u6587\u7ae0\u6765\u6e90(planckscale.info<\/a>)\u3001\u4f5c\u8005\u4fe1\u606f\u548c\u672c\u58f0\u660e\uff0c\u5426\u5219\u5c06\u8ffd\u7a76\u6cd5\u5f8b\u8d23\u4efb\u3002<\/strong><\/h5>\n

Levenberg-Marquardt\u7b97\u6cd5\uff08\u4e0b\u6587\u7b80\u79f0LM\u7b97\u6cd5\uff09\u901a\u5e38\u7528\u4e8e\u975e\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u6cd5\u7684\u76ee\u6807\u51fd\u6570\u6781\u5c0f\u5316\u3002\u8fd9\u662f\u4e00\u4e2a\u7f6e\u4fe1\u57df\u65b9\u6cd5\uff08Trust-Region Method\uff09\uff0c\u4e3a\u4e86\u9632\u6b62\u6b65\u957f\u592a\u5927\u800c\u8df3\u5230\u975e\u9884\u671f\u7684\u5c40\u90e8\u6781\u5c0f\u503c\uff0c\u8fd9\u7c7b\u7b97\u6cd5\u81ea\u9002\u5e94\u7684\u8c03\u6574\u6b65\u957f\u3002<\/p>\n

\u5047\u8bbe\"f(x)\"\u4e3a\u4e00\u4e2a\u5411\u91cf\u51fd\u6570\uff0c\u6bcf\u4e2a\u5206\u91cf\u90fd\u523b\u753b\u4e86\u4e00\u4e2a\u6837\u672c\u548c\u6a21\u578b\u9884\u6d4b\u4e4b\u95f4\u7684\u67d0\u79cd\u504f\u5dee\uff0c\u5219\u975e\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u76ee\u6807\u51fd\u6570\u4e3a<\/p>\n

(1) <\/span>   <\/span>\"\begin{eqnarray*}<\/p>\n

\u901a\u5e38\u57fa\u4e8e\u68af\u5ea6\u7684\u6570\u503c\u6781\u5c0f\u5316\u7b97\u6cd5\uff0c\u90fd\u662f\u7528\u4e00\u70b9\u7684\u5c40\u57df\u7279\u5f81\uff08\u5982\u5bfc\u6570\uff09\u5efa\u7acb\u8be5\u51fd\u6570\u53d8\u5316\u8d8b\u52bf\u7684\u6a21\u578b\uff0c\u4ee5\u6b64\u6765\u63a8\u6d4b\u4e00\u4e2a\u6700\u53ef\u53d6\u7684\u4e0b\u964d\u65b9\u5411\u548c\u6b65\u957f\u3002\u53d6\u4e00\u9636\u5bfc\u6570\u8fd1\u4f3c\u662f\u7ebf\u6027\u6a21\u578b\uff0c\u7528\u5207\u5e73\u9762\u6765\u8fd1\u4f3c\u51fd\u6570\u5728\u8be5\u70b9\u9644\u8fd1\u7684\u53d8\u5316\u8d8b\u52bf\uff1b\u53d6\u5230\u4e8c\u9636\u5bfc\u6570\u8fd1\u4f3c\u5219\u662f\u4e8c\u9636\u6a21\u578b\uff0c\u7528\u4e00\u4e2a\u629b\u7269\u9762\u6765\u8fd1\u4f3c\u3002\u5f53\u7136\uff0c\u4e5f\u53ef\u4ee5\u53d6\u5230\u66f4\u591a\u9636\uff0c\u6a21\u578b\u7684\u51e0\u4f55\u76f4\u89c2\u4e5f\u4f1a\u8d8a\u6765\u8d8a\u590d\u6742\uff0c\u8d8a\u6765\u8d8a\u7cbe\u786e\u7684\u903c\u8fd1\u771f\u5b9e\u7684\u51fd\u6570\u53d8\u5316\u8d8b\u52bf\uff0c\u4f46\u662f\u4f1a\u4ed8\u51fa\u66f4\u5927\u7684\u8ba1\u7b97\u4ee3\u4ef7\u3002\u5f53\u53d6\u5230\u65e0\u7a77\u9636\u65f6\uff0c\u6a21\u578b\u5728\u7ea7\u6570\u6536\u655b\u533a\u95f4\u5185\u53ef\u4ee5\u505a\u5230\u5b8c\u5168\u7cbe\u786e\u7684\u523b\u753b\u51fd\u6570\uff0c\u6b64\u65f6\u8fd9\u5c31\u662f\u6a21\u578b\u5c31\u662f\u51fd\u6570\u7684\u6cf0\u52d2\u5c55\u5f00\u4e86\u3002<\/p>\n

\u6211\u4eec\u628a\"f\"\u5728\u4efb\u4e00\u70b9\"x\"\u9644\u8fd1\u5c55\u5f00\"f(x+\delta x)=f(x)+J(x)\delta x\",\u8fd9\u6837\"E\"\u5728\"x\"\u9644\u8fd1\u5c31\u662f<\/p>\n

(2) <\/span>   <\/span>\"\begin{eqnarray*}<\/p>\n

\u6ce8\u610f\"J\"\u662f\"f\"\u800c\u975e\"E\"\u7684\u5bfc\u6570\uff0c\u8fd9\u91cc\u6211\u4eec\u5f97\u5230\u4e86\"E\"\u7684\u4e8c\u9636\u5c55\u5f00\uff0c\u5373\u7528\u4e00\u4e2a\u629b\u7269\u9762\u6765\u8fd1\u4f3c\u76ee\u6807\u51fd\u6570\"E\"\u5728\u4e00\u70b9\u9644\u8fd1\u7684\u5f62\u6001\u3002\u8fd9\u4e2a\u4e8c\u9636\u6a21\u578b\u663e\u7136\u662f\u4e00\u4e2a\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u2014\u2014\u8fd9\u6b63\u662f\u6211\u4eec\u6240\u8981\u7684\uff0c\u628a\u4e00\u4e2a\u975e\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u8f6c\u6362\u4e3a\u4e00\u7cfb\u5217\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\u6765\u6c42\u89e3\u3002<\/p>\n

\u56e0\u6b64\u4e00\u4e2a\u7b80\u5355\u76f4\u63a5\u7684\u60f3\u6cd5\u5c31\u662f\uff0c\u6bcf\u4e00\u8fed\u4ee3\u6b65\u6784\u9020\u8fd9\u6837\u4e00\u4e2a\u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u95ee\u9898\uff0c\u901a\u8fc7\u6781\u5c0f\u5316\u5b83\u4e0b\u964d\u5230\u4e0b\u4e00\u4e2a\u8fed\u4ee3\u70b9\uff0c\u5faa\u73af\u76f4\u5230\u6536\u655b\u3002\u4f46\u8fd9\u4e2a\u65b9\u6848\u663e\u7136\u6709\u95ee\u9898\u3002\u6211\u4eec\u7684\u4e8c\u9636\u5c55\u5f00\u6a21\u578b\u53ea\u80fd\u5728\u4e00\u4e2a\u5c0f\u90bb\u57df\u4e0a\u6709\u6548\uff0c\u5f53\"\delta x\"\u589e\u5927\u65f6\uff0c\u88ab\u6211\u4eec\u5ffd\u7565\u6389\u7684\u9ad8\u9636\u9879\u5c31\u4f1a\u8d8a\u6765\u8d8a\u660e\u663e\uff0c\u6700\u540e\u8ba9\u4e8c\u9636\u6a21\u578b\u5f7b\u5e95\u5931\u6548\u3002\u8fd9\u6837\uff0c\u76f4\u63a5\u6839\u636e\u4e8c\u9636\u6a21\u578b\u8ba1\u7b97\u51fa\u6765\u7684\u8fed\u4ee3\u70b9\u5bf9\u76ee\u6807\u51fd\u6570\u800c\u8a00\u53ef\u80fd\u5e76\u975e\u6211\u4eec\u60f3\u8981\u7684\uff0c\u5b83\u7684\u51fd\u6570\u503c\u53ef\u80fd\u6bd4\u4e0a\u4e00\u70b9\u8fd8\u8981\u9ad8\uff08\u56e0\u800c\u76ee\u6807\u51fd\u6570\u4e0d\u964d\u53cd\u589e\uff09\uff1b\u4e5f\u53ef\u80fd\u5c3d\u7ba1\u6bd4\u4e0a\u4e00\u70b9\u4e0b\u964d\u4e86\u4f46\u662f\u5374\u8df3\u5230\u4e86\u53e6\u4e00\u4e2a\u6211\u4eec\u4e0d\u60f3\u8981\u7684\u51f8\u533a\u57df\u91cc\uff08\u56e0\u800c\u7b97\u6cd5\u4f1a\u6536\u655b\u5230\u79bb\u521d\u59cb\u731c\u6d4b\u89e3\u66f4\u8fdc\u7684\u5c40\u90e8\u6781\u5c0f\u503c\u70b9\u4e0a\uff09\uff1b\u66f4\u4e25\u91cd\u7684\u60c5\u51b5\uff0c\u6a21\u578b\u751a\u81f3\u53ef\u80fd\u662f\u9000\u5316\u7684\uff0c\u5373\u4e00\u79cd\u6781\u7aef\u5f62\u5f0f\u7684\u629b\u7269\u9762\u2014\u2014\u5c31\u50cf\u4e00\u672c\u88ab\u534a\u5377\u8d77\u7684\u4e66\uff0c\u6b64\u65f6\u6211\u4eec\u5728\u5f2f\u6298\u7684\u65b9\u5411\u4ecd\u80fd\u627e\u5230\u6781\u5c0f\u503c\uff0c\u4f46\u5728\u5176\u5782\u76f4\u65b9\u5411\u5df2\u7ecf\u65e0\u6cd5\u627e\u5230\u6781\u5c0f\u503c\uff08\u6216\u8005\u8bf4\u5904\u5904\u6781\u5c0f\uff09\u3002<\/p>\n

\u4e3a\u4e86\u89e3\u51b3\u4ee5\u4e0a\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u7ed9\u6a21\u578b\u52a0\u5165\u4e00\u4e9b\u7ea6\u675f\uff0c\u628a\u8fed\u4ee3\u6b65\u957f\u7ea6\u675f\u5728\u4e00\u4e2a\u5408\u7406\u7684\u8303\u56f4\u5185\uff0c\u4fdd\u8bc1\u5728\u8fd9\u4e2a\u8303\u56f4\u5185\u6a21\u578b\u8db3\u591f\u6709\u6548\u3002\u540c\u65f6\uff0c\u6211\u4eec\u4e5f\u5e0c\u671b\u5728\u4e8c\u9636\u6a21\u578b\u9000\u5316\u7684\u65f6\u5019\uff0c\u7ea6\u675f\u80fd\u591f\u62ef\u6551\u5b83\uff0c\u4fdd\u8bc1\u7b97\u6cd5\u603b\u80fd\u6c42\u51fa\u4e00\u4e2a\u6781\u5c0f\u503c\u3002\u8fd9\u4e2a\u7ea6\u675f\u5f88\u7b80\u5355\uff0c\u5982\u4e0b<\/p>\n

(3) <\/span>   <\/span>\"\begin{eqnarray*}<\/p>\n

\u6211\u4eec\u52a0\u5165\u4e86\u4e00\u4e2a\u4e8c\u6b21\u7ea6\u675f\u9879\u3002\u5355\u72ec\u770b\u8be5\u9879\uff0c\u5b83\u662f\u4e00\u4e2a\u4e2d\u5fc3\u5728\"x\"\u70b9\uff0c\u5f00\u53e3\u5411\u4e0a\u7684\u629b\u7269\u9762\uff0c\u6216\u8005\u8bf4\u4e00\u4e2a\u4e8c\u6b21\u52bf\u9631\u3002\u8fd9\u4e2a\u52bf\u9631\u50cf\u4e00\u4e2a\u7b8d\uff0c\u628a\"\delta x\"\u7b8d\u5728\"x\"\u70b9\u9644\u8fd1\u7684\u5c0f\u90bb\u57df\u4e2d\u3002\u901a\u8fc7\u8c03\u8282\"\lambda\"\u53ef\u4ee5\u589e\u5f3a\u6216\u51cf\u5f31\u5b83\u5bf9\"\delta x\"\u7684\u7ea6\u675f\uff1a\u5f53\"\lambda\"\u5145\u5206\u5927\u65f6\uff0c\u7ea6\u675f\u9879\u6210\u4e3a\u4e3b\u8981\u8d21\u732e\u9879\uff0c\u8fd9\u65f6\u6a21\u578b\u603b\u6709\u4e00\u4e2a\u6781\u5c0f\u503c\uff0c\u4e14\u6b65\u957f\u8f83\u5c0f\uff1b\u5f53\"\lambda\"\u8f83\u5c0f\u65f6\uff0c\u7ea6\u675f\u9879\u51e0\u4e4e\u53ef\u4ee5\u5ffd\u7565\uff0c\u7b97\u6cd5\u4ee5\u5927\u6b65\u957f\u5feb\u901f\u5f80\u6781\u5c0f\u503c\u63a5\u8fd1\u3002<\/p>\n

\u518d\u6765\u770b\u77e9\u9635\"C(x)\". \u8fd9\u4e2a\u77e9\u9635\u901a\u5e38\u88ab\u8bbe\u7f6e\u4e3a\u5bf9\u89d2\u7684\u3002\u6b64\u65f6\uff0c<\/p>\n

(4) <\/span>   <\/span>\"\begin{eqnarray*}<\/p>\n

\"\transp{C}C\"\u7684\u672c\u5f81\u503c\u63a7\u5236\u7740\u6bcf\u4e2a\u65b9\u5411\u4e0a\u629b\u7269\u9762\u4e0a\u5347\u7684\u5feb\u6162\u3002\u53ef\u89c1\uff0c\u5982\u679c\u4e00\u4e2a\u65b9\u5411\u76f8\u5e94\u7684\u672c\u5f81\u503c\u88ab\u8bbe\u7f6e\u7684\u8f83\u5c0f\uff0c\u90a3\u4e48\u8be5\u65b9\u5411\u7684\u7ea6\u675f\u9879\u4e0a\u5347\u7f13\u6162\uff0c\u7ea6\u675f\u8f83\u5f31\uff0c\u6b65\u957f\u8de8\u5ea6\u8f83\u5927\uff1b\u5426\u5219\u53cd\u4e4b\u3002\u73b0\u5b9e\u4e2d\u4f7f\u7528\u7684\u6a21\u578b\uff0c\u76ee\u6807\u51fd\u6570\u5bf9\u4e8e\u5404\u4e2a\u53c2\u6570\u7684\u654f\u611f\u5ea6\u4e0d\u540c\uff0c\u6709\u7684\u53c2\u6570\u7565\u5fae\u8c03\u6574\u5c31\u53ef\u4ee5\u5bfc\u81f4\u76ee\u6807\u51fd\u6570\u7684\u5f3a\u70c8\u53d8\u5316\uff0c\u6709\u7684\u5219\u53cd\u4e4b\u3002\"C(x)\"\u8fd9\u4e2a\u53c2\u6570\u77e9\u9635\u4f7f\u5f97\u6211\u4eec\u53ef\u4ee5\u9488\u5bf9\u5404\u4e2a\u4e0d\u540c\u7684\u53c2\u6570\u8bbe\u7f6e\u4e0d\u540c\u7a0b\u5ea6\u7684\u6b65\u957f\u7ea6\u675f\uff0c\u4ece\u800c\u80fd\u591f\u6784\u9020\u51fa\u4e00\u4e2a\u7a33\u5b9a\u7684\u7b97\u6cd5\u3002<\/p>\n

\uff08\u672a\u5b8c\u5f85\u8865\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"

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