多元多项式函数的极值  

Extremum of Multivariate Polynomial Function

作　　者：张文哲 ZHANG Wen-zhe(Department of Science,College of Arts and Sciences,Hubei Normal University,Huangshi Hubei 435109,China)

机构地区：[1]湖北师范大学文理学院理学部,湖北黄石435109

出　　处：《大学数学》2020年第3期83-89,共7页College Mathematics

摘　　要：多元函数求极值的方法已经众所周知,然而对于一些结构较为复杂的函数,无法求得它的极值,甚至一些驻点都无法得到.本文系统地讨论了多元多项式函数的极值求法,包括自由极值和条件极值.可以看到关键在于解多元多项式方程组,由于比较关心它们的符号解,因此使用了Maple软件,它对于计算帮助很大.The method to find the extremum of multivariate function is well known,but for some functions with complicated structure,we can not find their extrema,even the stationary points we can not get.In this paper,we discuss the method to find the extremum of multivariate polynomial function systematically,including free extremum and conditional extremum.We can see that the key is to solve the systems of multivariate polynomial equations.Since we are more interested in the symbolic solutions,we use the Maple software,it is a great help to our calculation.

关 键 词：多元多项式 极值 方程求解 

分 类 号：O172.1[理学—数学]