| 基于H-张量的齐次多项式正定性的判定 |
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| 引用本文： | 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. |
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| 作者姓名： | 孙德淑 柏冬健 王峰 |
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| 作者单位： | 贵州民族大学 数据科学与信息工程学院,贵州 贵阳 550025 |
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| 基金项目： | 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) |
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| 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.
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| 关 键 词： | 齐次多项式 H-张量 正定性 对角占优性 |
| 收稿时间： | 2020-06-15 |
New criteria based H-tensors for identifying the positive definiteness of multivariate homogeneous forms |
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| 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. |
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| Authors: | SUN De-shu BAI Dong-jian WANG Feng |
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| Institution: | College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025 |
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| 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. |
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| Keywords: | homogeneous polynomial H-tensors positive definiteness diagonally dominant |
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