多元函数高阶差商公式

High Order Difference Quotient Formulas of Multivariate Functions

为了将函数逼近论的主要成果有针对性地向多元函数进行拓广,利用组合公式的某些技巧做出的工作如下:1)建立了多元函数高阶差商公式的统一表达式;2)证明了高阶方向导数的差商公式;3)研究了近似高阶偏导数;4)给出了多元函数二阶偏导数及Hessian阵中心差商的截断误差.

To promote the main results of function approximation theory to the multivariate function,the following work was presented in this paper by some skills of combination formula: the unified expression of the high order difference quotient formulas of multivariate function was established;the difference formula of the high order directional derivative was proven;the approximate high order partial derivative was studied;and the second-order partial derivative of the multivariate function and the truncation errors of the center difference quotient of the Hessian matrix were given.