多元函数高阶差商公式  

High Order Difference Quotient Formulas of Multivariate Functions

作　　者：隋允康[1] 铁军[2] SUI Yunkang;TIE Jun(College of Mechanical Engineering and Applied Electronics Technology,Beijing University of Technology,Beijing 100124,China;School of Polytechnic,Tianjin University of Finance and Economics,Tianjin 300222,China)

机构地区：[1]北京工业大学机械工程与应用电子技术学院,北京100124 [2]天津财经大学理工学院,天津300222

出　　处：《北京工业大学学报》2019年第11期1077-1081,共5页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11672103)

摘　　要：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.

关 键 词：高阶差商 Hessian阵 高阶偏导数 数学模型的建立 

分 类 号：O343.1[理学—固体力学] O17[理学—力学]