基于H-张量的齐次多项式正定性的判定

兰州理工大学学报 ›› 2021, Vol. 47 ›› Issue (5): 155-161.

基于H-张量的齐次多项式正定性的判定

孙德淑^*, 柏冬健, 王峰

贵州民族大学数据科学与信息工程学院, 贵州贵阳 550025

收稿日期:2020-06-15 出版日期:2021-10-28 发布日期:2021-11-18
通讯作者: 孙德淑(1980-),女,山东临沂人,硕士,讲师.Email:sundeshu0818@163.com
基金资助:
国家自然科学基金(11861077),贵州省科学技术基金(20181079,20191161),贵州省教育厅自然科学基金(2015420)

New criteria based H-tensors for identifying the positive definiteness of multivariate homogeneous forms

SUN De-shu, BAI Dong-jian, WANG Feng

College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025

Received:2020-06-15 Online:2021-10-28 Published:2021-11-18

摘要/Abstract

摘要： 通过构造不同的正对角阵,结合不等式的放缩技巧,给出了H-张量比较实用的新判别条件.作为应用,给出了判定偶次齐次多项式正定性的新方法,用数值算例说明新方法的可行性.

关键词: 齐次多项式, H-张量, 正定性, 对角占优性

Abstract: Some practical conditions for H-tensors are provided by constructing different positive diagonal matrices and applying some techniques of inequalities. As applications, new methods for the positive definiteness of even-order homogeneous multivariate polynomial are presented. Numerical examples are given to illustrate the feasibility of the new method.

Key words: homogeneous polynomial, H-tensors, positive definiteness, diagonally dominant

中图分类号:

O151.21

孙德淑, 柏冬健, 王峰. 基于H-张量的齐次多项式正定性的判定[J]. 兰州理工大学学报, 2021, 47(5): 155-161.

SUN De-shu, BAI Dong-jian, WANG Feng. New criteria based H-tensors for identifying the positive definiteness of multivariate homogeneous forms[J]. Journal of Lanzhou University of Technology, 2021, 47(5): 155-161.

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