“Hessian”的概念、定义、翻译、参考文献-科学参考

Hessian

Mathematics

单词	Hessian
释义	Hessian Mathematics The Hessian of a differentiable function f(x,y) of two variables is the matrix $H = (\begin{matrix} f_{x x} & f_{x y} \\ f_{y x} & f_{y y} \end{matrix}) .$ If the partial derivatives are continuous functions, then the mixed derivatives are equal and so H is symmetric. The Hessian appears in the Taylor series of f as $\begin{array}{l} f (x + h, y + k) \\ = f (x, y) + (h f_{x} + k f_{y}) + \frac{1}{2} (h^{2} f_{x x} + 2 h k f_{x y} + k^{2} f_{y y}) + \dots \\ = f (x, y) + (h f_{x} + k f_{y}) + \frac{1}{2} (h, k) H (\begin{matrix} h \\ k \end{matrix}) + \dots \end{array}$ and is used in the classification of stationary points which are non-degenerate; that is detH ≠ 0.
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