| 基于n次型正定性的多元函数极值判别法 |
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| 引用本文： | 叶振信,张浩明,杨锐,冯志刚.基于n次型正定性的多元函数极值判别法[J].数学的实践与认识,2014(23). |
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| 作者姓名： | 叶振信 张浩明 杨锐 冯志刚 |
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| 作者单位： | 中国运载火箭技术研究院 |
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| 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.
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| 关 键 词： | n元函数 极值 n次型 正定性 Taylor定理 |
A Judgement Method for Extreme Value of Multivariate Functions Based on the Positive Definite Property of nth Degree Form |
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| Abstract: | For the situation that the second-order partial derivatives of the multivariate function are 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. |
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| Keywords: | multivariate functions extreme value nth degree form positive definite property Taylor's theorem |
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