\u4e09\u7ef4\u5e73\u9762\u7684\u8868\u8fbe\u65b9\u5f0f\u6709\u5f88\u591a\u79cd\uff0c\u901a\u5e38\u91c7\u7528\u7684\u5f62\u5f0f\u4e3a$$Ax+By+Cz+D=0$$\u5176\u4e2d\\(\\begin{bmatrix}A\\\\B\\\\C\u00a0\\end{bmatrix}\\)\u4e3a\u5e73\u9762\u6cd5\u5411\u91cf\u3002<\/p>\n
\u5df2\u77e5\uff1a\u91c7\u6837\u70b9\u96c6\\(\\{(x_1,y_1),(x_2,y_2),…,(x_n,y_n)\\}\\),\u6b32\u6c42\u4e00\u5e73\u9762\\(p\\),\u4f7f\u5f97\u6240\u6709\u91c7\u6837\u70b9\u5230\\(p\\)\u7684\u8ddd\u79bb\u7684\u5e73\u65b9\u548c\\(f\\)\u6700\u5c0f\u3002 \u4e09\u7ef4\u5e73\u9762\u7684\u8868\u8fbe\u65b9\u5f0f\u6709\u5f88\u591a\u79cd\uff0c\u901a\u5e38\u91c7\u7528\u7684\u5f62\u5f0f\u4e3a$$Ax+By+Cz+D=0$$\u5176\u4e2d … Continue reading
\n$$f=\\sum_{i=1}^n\u00a0(\\frac{|Ax_i+By_i+Cz_i+D|}{\\sqrt{A^2+B^2+C^2}})^2$$
\n\u56e0\u4e3a\\(A,B,C\\)\u7684\u5173\u8054\u6027\uff0c\u6211\u4eec\u53ef\u4ee5\u4ee4\\(||(A,B,C)^T||=1\u3002\\)\u90a3\u4e48
\n$$f\u00a0=\u00a0\\sum(Ax_i+By_i+Cz_i+D)^2$$
\n\u8fd9\u4e0e\u4e8c\u7ef4\u76f4\u7ebf\\(Ax+By+C=0\\)\u7684\u60c5\u51b5\u4e00\u6a21\u4e00\u6837\uff0c\u5177\u4f53\u89e3\u6cd5\u53ef\u4ee5\u53c2\u8003\u6211\u7684\u53e6\u5916\u4e00\u7bc7\u5e16\u5b50<\/a>\u3002
\n\u4e3b\u8981\u601d\u8def\u662f\uff1a
\n\u9996\u5148\u89e3D\u3002\u4ee4\\(\\frac\u00a0{\\partial\u00a0f\u00a0}{\\partial\u00a0D}=\\sum2(Ax_i+By_i+Cz_i+D)\u00a0=0\\),\u53ef\u4ee5\u5f97\u5230\\(D\u00a0=\u00a0-\\frac{\\sum\u00a0(Ax_i+By_i+Cz_i)}{n}\u00a0\\)\u3002
\n\u4ee4\\(Y_i\u00a0=\u00a0X_i\u00a0-\\bar\u00a0X\\),\u5219\u00a0\\(f=\\sum(Ay_i+By_i+Cz_i)^2\\)
\n$$(f=\\begin{bmatrix}A\\\\B\\\\C\\end{bmatrix}^T\\begin{bmatrix}\\sum\u00a0x_2\u00a0&\u00a0\\sum\u00a0xy\u00a0&\u00a0\\sum\u00a0xz\\\\\u00a0\\sum\u00a0xy\u00a0&\u00a0\\sum\u00a0y^2\u00a0&\u00a0\u00a0\\sum\u00a0yz\\\\\u00a0\\sum\u00a0xz\u00a0&\u00a0\\sum\u00a0yz\u00a0&\u00a0\\sum\u00a0z^2\\end{bmatrix}\\begin{bmatrix}A\\\\B\\\\C\\end{bmatrix}$$
\n\u56e0\u4e3a\u9650\u5b9a\u6761\u4ef6\\(||(A,B,C)^T||=1\u3002\\)\u4ee5\u53ca\u4e2d\u95f4\u7684\u77e9\u9635\u4e3a\u5b9e\u5bf9\u79f0\u77e9\u9635\uff0c\u4e0a\u8ff0\u8868\u8fbe\u5f0f\u53d6\u6700\u5c0f\u503c\u65f6\u7684\\(A,B,C\\)\u503c\u5bf9\u5e94\u4e2d\u95f4\u77e9\u9635\u7684\u6700\u5c0f\u7279\u5f81\u503c\u7684\u6700\u5c0f\u7279\u5f81\u5411\u91cf\u3002\u91c7\u7528Eigen\u7684EigenSolver<\/a>\u53ef\u4ee5\u7f16\u7a0b\u6c42\u89e3\u3002
\n\u8be6\u7ec6\u8bf4\u660e\u53ef\u4ee5\u53c2\u8003\u8fd9\u91cc<\/a>\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"