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x=\"889\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(10891,0)\"><g transform=\"translate(-15,0)\"><g transform=\"translate(0,-97)\"><use xlink:href=\"#E185-MJMATHI-66\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(550,0)\"><use xlink:href=\"#E185-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(389,0)\"><use xlink:href=\"#E185-MJMATHI-61\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMAIN-2B\" x=\"751\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMATHI-68\" x=\"1751\" y=\"0\"><\/use><\/g><use xlink:href=\"#E185-MJMAIN-29\" x=\"2716\" y=\"0\"><\/use><\/g><use xlink:href=\"#E185-MJMAIN-2248\" x=\"3933\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMATHI-66\" x=\"4989\" y=\"0\"><\/use><g transform=\"translate(5539,0)\"><use xlink:href=\"#E185-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMATHI-61\" x=\"389\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMAIN-29\" x=\"918\" y=\"0\"><\/use><\/g><use xlink:href=\"#E185-MJMAIN-2B\" x=\"7068\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMATHI-66\" x=\"8068\" y=\"0\"><\/use><g transform=\"translate(8785,0)\"><g transform=\"translate(0,412)\"><use transform=\"scale(0.707)\" xlink:href=\"#E185-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E185-MJMAIN-31\" x=\"389\" y=\"0\"><\/use><use transform=\"scale(0.707)\" xlink:href=\"#E185-MJMAIN-29\" x=\"888\" y=\"0\"><\/use><\/g><\/g><g transform=\"translate(9955,0)\"><use xlink:href=\"#E185-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMATHI-61\" x=\"389\" y=\"0\"><\/use><use xlink:href=\"#E185-MJMAIN-29\" x=\"918\" y=\"0\"><\/use><\/g><use xlink:href=\"#E185-MJMATHI-68\" x=\"11262\" y=\"0\"><\/use><\/g><\/g><\/g><\/g><\/svg><\/span><\/div>\n<p><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-4\">{f{ \\left( {a+h} \\right) } \\approx f{ \\left( {a} \\right) }+f\\mathop{{}}\\nolimits^{{ \\left( 1 \\right) }}{ \\left( {a} \\right) }h}<\/script><\/div>\n<\/div>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;\u73b0\u6709\u5982\u4e0b\u9898\u76ee\uff1a\u5bf9\u4e8esin(-1:0.25:0.5)\uff0c\u4f7f\u7528\u6cf0\u52d2\u516c\u5f0f\u4f30\u8ba1sin(0.5005)\u7684\u503c\u3002<\/p>\n<pre><code>%% Section 01\ny = sin(-1:0.25:0.5);\nyg = gradient(y, 0.25);\ny_guess = y(end) + yg(end)*(0.5005 - 0.5);\ndisp(&quot;\u9884\u6d4b\u7ed3\u679c\uff1a&quot;);\ndisp(y_guess);\ndisp(&quot;\u5b9e\u9645\u7ed3\u679c\uff1a&quot;);\ndisp(sin(0.5005));\n<\/code><\/pre>\n<h2 >1.2 \u591a\u5143\u51fd\u6570\u6761\u4ef6\u6781\u503c<\/h2>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;\u5bf9\u4e8e\u76ee\u6807z = f(x, y)\uff0c\u6211\u4eec\u6709\u6761\u4ef6\u03c6(x, y) = 0\u3002\u5219\u4f18\u5316\u95ee\u9898\u53ef\u4ee5\u8f6c\u6362\u4e3a\uff1a<\/p>\n<div contenteditable=\"true\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n11\" cid=\"n11\" mdtype=\"math_block\">\n<div class=\"md-rawblock-container md-math-container\" contenteditable=\"false\" 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y=\"0\"><\/use><\/g><\/g><\/g><\/g><\/g><\/svg><\/span><\/div>\n<p><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-30\">{L=f{ \\left( {x,y} \\right) }+ \\lambda  \\varphi { \\left( {x,y} \\right) }}<\/script><\/div>\n<\/div>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;\u63a5\u4e0b\u6765\u6211\u4eec\u53ea\u9700\u8981\u5bf9L\u4e2d\u7684x,y\u548c\u03c6\u6c42\u504f\u5bfc\u5373\u53ef\uff1a<\/p>\n<div contenteditable=\"true\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n82\" cid=\"n82\" mdtype=\"math_block\">\n<div class=\"md-rawblock-container md-math-container\" contenteditable=\"false\" tabindex=\"-1\">\n<div class=\"MathJax_SVG_Display\"><span class=\"MathJax_SVG\" id=\"MathJax-Element-31-Frame\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" width=\"77.282ex\" height=\"11.936ex\" viewBox=\"0 -2831.6 33274.1 5139.2\" role=\"img\" focusable=\"false\" 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xlink:href=\"#E202-MJMATHI-67\" x=\"9526\" y=\"0\"><\/use><g transform=\"translate(10172,0)\"><use transform=\"scale(0.707)\" xlink:href=\"#E202-MJMATHI-54\" x=\"0\" y=\"583\"><\/use><\/g><g transform=\"translate(10937,0)\"><use xlink:href=\"#E202-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(389,0)\"><use xlink:href=\"#E202-MJMATHI-58\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(852,0)\"><use transform=\"scale(0.707)\" xlink:href=\"#E202-MJMATHI-6B\" x=\"0\" y=\"-213\"><\/use><\/g><\/g><use xlink:href=\"#E202-MJMAIN-29\" x=\"1709\" y=\"0\"><\/use><\/g><use xlink:href=\"#E202-MJMATHI-3B4\" x=\"13035\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMAIN-2B\" x=\"13709\" y=\"0\"><\/use><use xlink:href=\"#E202-MJMATHI-3B4\" x=\"14709\" y=\"0\"><\/use><g transform=\"translate(15326,0)\"><use transform=\"scale(0.707)\" xlink:href=\"#E202-MJMATHI-54\" x=\"0\" y=\"583\"><\/use><\/g><use xlink:href=\"#E202-MJMATHI-48\" x=\"16091\" y=\"0\"><\/use><g transform=\"translate(16979,0)\"><use xlink:href=\"#E202-MJMAIN-28\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(389,0)\"><use xlink:href=\"#E202-MJMATHI-58\" x=\"0\" y=\"0\"><\/use><g transform=\"translate(852,0)\"><use transform=\"scale(0.707)\" xlink:href=\"#E202-MJMATHI-6B\" x=\"0\" y=\"-213\"><\/use><\/g><\/g><use xlink:href=\"#E202-MJMAIN-29\" x=\"1709\" y=\"0\"><\/use><\/g><use xlink:href=\"#E202-MJMATHI-3B4\" x=\"19077\" y=\"0\"><\/use><\/g><\/g><\/g><\/g><\/svg><\/span><\/div>\n<p><script type=\"math\/tex; mode=display\" id=\"MathJax-Element-20\">\n{f{ \\left( {X\\mathop{{}}\\nolimits_{{k}}+ \\delta } \\right) } \\approx f{ \\left( {X\\mathop{{}}\\nolimits_{{k}}} \\right) }+g\\mathop{{}}\\nolimits^{{T}}{ \\left( {X\\mathop{{}}\\nolimits_{{k}}} \\right) } \\delta + \\delta \\mathop{{}}\\nolimits^{{T}}H{ \\left( {X\\mathop{{}}\\nolimits_{{k}}} \\right) } \\delta }\n<\/script><\/div>\n<\/div>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;g(x<sub>k<\/sub>) = 0\u7684\u70b9\u4e3a\u5e73\u7a33\u70b9\uff08\u5019\u9009\u70b9\uff09\uff0c\u5982\u679c\u6709H(x<sub>k<\/sub>)&gt;0\uff0c\u5219\u70b9x<sub>k<\/sub>\u4e3a\u4e25\u683c\u5c40\u90e8\u6781\u5c0f\u70b9\uff08\u53cd\u4e4b\u4e3a\u4e25\u683c\u5c40\u90e8\u6700\u5927\u70b9\uff09\uff0c\u5982\u679cH(x<sub>k<\/sub>)\u4e3a\u4e0d\u5b9a\u77e9\u9635\uff0c\u5219x<sub>k\u662f\u4e00\u4e2a\u978d\u70b9\u3002<\/p>\n<h2 >2.5 \u65e0\u7ea6\u675f\u4f18\u5316\u8fed\u4ee3\u6cd5<\/h2>\n<pre><code>    \u8fed\u4ee3\u6cd5\u57fa\u672c\u7ed3\u6784\uff08\u6700\u5c0f\u5316f(x)\uff09\uff1a\n1\uff1a\u9009\u62e9\u4e00\u4e2a\u521d\u59cb\u70b9\uff0c\u8bbe\u7f6e\u4e00\u4e2aconvergence tolerance \u03c4\uff0c\u8ba1\u6570k\u3002\n2\uff1a\u51b3\u5b9a\u641c\u7d22\u65b9\u5411dk\uff0c\u4f7f\u5f97\u51fd\u6570\u4e0b\u964d\u3002\n3\uff1a\u6784\u5efaxk+1 = xk+1 + \u03b1kdk\uff0c\u5176\u4e2d\u03b1\u79f0\u4e3a\u6b65\u957f\u6216\u662f\u5b66\u4e60\u901f\u7387\u3002\n4\uff1a\u5982\u679c||d||2 &lt; \u03c4\uff0c\u5219\u8f93\u51fa\u89e3\uff0c\u5426\u5219\u91cd\u590d\u76f4\u5230\u6536\u655b\u3002\n<\/code><\/pre>\n<h3 >2.5.1 \u68af\u5ea6\u4e0b\u964d\u6cd5<\/h3>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;\u65b9\u5411\u9009\u53d6\uff1ad<sub>k<\/sub> = -g(x<sub>k<\/sub>)<\/p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;\u5bf9\u4e8e\u4ee5\u4e0a\u7b97\u6cd5\uff0c\u4e3b\u8981\u95ee\u9898\u5728\u4e8e\u5982\u4f55\u786e\u5b9ad<sub>k<\/sub>\uff0c\u5bf9\u4e8e\u4e00\u9636\u5bfc\u6570\u7684\u60c5\u51b5\uff0cd<sub>k<\/sub> = -g(x<sub>k<\/sub>)\uff0c\u4e0b\u9762\u7ed9\u51fa\u8bc1\u660e\uff1a<\/p>\n<div contenteditable=\"true\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n61\" cid=\"n61\" mdtype=\"math_block\">\n<div class=\"md-rawblock-container md-math-container\" tabindex=\"-1\">\n<div class=\"MathJax_SVG_Display\"><span class=\"MathJax_SVG\" id=\"MathJax-Element-21-Frame\" tabindex=\"-1\" style=\"font-size: 100%; display: inline-block;\"><svg 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