基于n次型正定性的多元函数极值判别法  

A Judgement Method for Extreme Value of Multivariate Functions Based on the Positive Definite Property of nth Degree Form

作　　者：叶振信 张浩明[1] 杨锐[1] 冯志刚[2] 

机构地区：[1]中国运载火箭技术研究院北京宇航系统工程研究所,北京100076 [2]国防科学技术大学航天与材料工程学院,湖南长沙410073

出　　处：《数学的实践与认识》2014年第23期303-306,共4页Mathematics in Practice and Theory

摘　　要：针对多元函数稳定点处二阶偏导数全为0的情况,提出了有效的极值判别法.定义了广义n维方阵、n次型及其正定性;提出了更具普遍意义的极值充分条件;得到了利用n次型的正定性判断n元函数极值的方法并举例验证了结论的正确性和有效性.For the situation that the second-order partial derivatives of the multivariate function axe all zeros at the stable point, this paper presents an effective judgement method for extreme value. Firstly we defined the generalized square matrix of n dimensions, the nth degree form and its positive definite property. And then we put forward a more universal sufficient condition about extreme value. Further more, by using the positive definite property of the nth degree form, we obtained a judgement method for extreme value. Finally, the results were proved to be correct and effective in some examples.

关 键 词：N元函数 极值 n次型 正定性 TAYLOR定理 

分 类 号：O174[理学—数学]