海森矩阵(Hessian matrix 或 Hessian)

海森矩阵Hessian matrix 或 Hessian)是一个自变量为向量的实值函数的二阶偏导数组成的方块矩阵,此函数如下:

f(x_1, x_2, \dots, x_n),

如果 f 所有的二阶导数都存在,那么 f 的海森矩阵即:

H(f)ij(x) = DiDjf(x)

其中 x = (x_1, x_2, \dots, x_n),即

H(f) = \begin{bmatrix}
\frac{\partial^2 f}{\partial x_1^2} & \frac{\partial^2 f}{\partial x_1\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_1\,\partial x_n} \\  \\
\frac{\partial^2 f}{\partial x_2\,\partial x_1} & \frac{\partial^2 f}{\partial x_2^2} & \cdots & \frac{\partial^2 f}{\partial x_2\,\partial x_n} \\  \\
\vdots & \vdots & \ddots & \vdots \\  \\
\frac{\partial^2 f}{\partial x_n\,\partial x_1} & \frac{\partial^2 f}{\partial x_n\,\partial x_2} & \cdots & \frac{\partial^2 f}{\partial x_n^2}
\end{bmatrix}
posted @ 2011-11-28 13:35  Greenbird  Views(514)  Comments(0Edit  收藏  举报

To further demonstrate the capabilities of KinFu Large Scale, we made another example with a room.