基于Hessian矩阵的多元函数极值问题  

Study on Extreme Value Problem of Multivariate Function based on Hessian matrix

作　　者：张梅荣[1] 

机构地区：[1]北京印刷学院,北京102600

出　　处：《北京印刷学院学报》2013年第6期80-82,共3页Journal of Beijing Institute of Graphic Communication

基　　金：2013年北京印刷学院校级教学改革重点项目资助;2013年北京印刷学院学科与研究生教育专项资金资助;北京印刷学院校级重点资助项目(E-a-2012-31)

摘　　要：极值问题是应用数学的重要内容之一,针对这一问题进行了讨论,介绍了对称矩阵、正定矩阵和Hessian矩阵,针对工科类本科高等数学教材中没有介绍的三元及以上函数的极值问题和条件极值问题中驻点的进一步判别,给出了相应的判别定理,并结合具体实例,进一步展示如何运用判别定理。Extreme value problem is one of the important contents in engineering advanced mathematics, This paper discusses the extreme value problem of multivariate function. The author introduces the basic knowledge of symmetric matrix, positive definite matrix and Hessian matrix etc. It gives the corresponding discriminant theorems about extreme value problem of three variables above function and the stagnation point discrimination of conditional extremum problem which have not been included in textbooks, and combines with specific examples to show how to use discriminant theorems.

关 键 词：对称矩阵 正定矩阵 HESSIAN矩阵 多元函数极值 

分 类 号：O175.25[理学—数学]