Hessian技术
令C =C(w),假设目标是最小化函数C 根据泰勒公式得:
\begin{eqnarray}
C(w+\Delta w) & = & C(w) + \sum_j \frac{\partial C}{\partial w_j} \Delta w_j
\nonumber \\ & & + \frac{1}{2} \sum_{jk} \Delta w_j \frac{\partial^2 C}{\partial w_j
\partial w_k} \Delta w_k + \ldots
\tag{103} \\
& = & C(w) + \nabla C \cdot \Delta w +
\frac{1}{2} \Delta w^T H \Delta w + \ldots,
\tag{104}\end{eqnarray}
\begin{eqnarray}
C(w+\Delta w) \approx C(w) + \nabla C \cdot \Delta w +
\frac{1}{2} \Delta w^T H \Delta w.
\tag{105}\end{eqnarray}
因此,基于Hessian技术,w的更新的策略为:
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