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齐次多项式正定性的新判定准则

New Criteria for the Positive Definiteness of Multivariate Homogeneous Forms
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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,得到了H-张量新的判别方法.作为应用,给出了判定偶次齐次多项式正定性的新条件,数值算例表明了新方法的可行性. We provided some new practical criterion for H-tensors by constructing different positive diagonal matrices and applying some techniques of inequalities.As applications,this paper has presented new methods for identifying the positive definiteness of even-order homogeneous multivariate forms.Numerical examples have illustrated advantages of new results.
作者 赵鹏程 王峰 ZHAO Pengcheng;WANG Feng(Data Science and Information Engineering School of Guizhou Minzu University,Guiyang Guizhou 550025,China)
机构地区 贵州民族大学数据科学与信息工程学院
出处 《四川文理学院学报》 2022年第5期20-31,共12页 Sichuan University of Arts and Science Journal
基金 贵州省科学技术基金([2018]1079,[2019]1161) 贵州民族大学自然科学基金(GZMU[2019]YB08)。
关键词 齐次多项式 H-张量 正定性 不可约 非零元素链 homogeneous multivariate form tensors positive definiteness irreducible nonzero elements chain
分类号 O151.21 [理学—基础数学]
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  • 3YANG Yuning, YANG Qingzhi. Fruther results for Perron-Frobenius theorem for nonnegative tensors [J]. SIAM Journal on Matrix Analysis and Applications, 2010, 31(5): 2517-2530.
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  • 6WANG Feng, SUN Deshu, ZHAO Jianxing, LI Chaoqian. New practical criteria for H-tensors and its application [J]. submitted to Linear and Multilinear Algebra.
  • 7QI Liqun, WANG Fei, WANG Yiju. Z-eigenvalue methods for a global polynomial optimization problem [J]. Mathematical Programming, 2009, 118(2): 301-316.
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  • 10ZHANG Liping, QI Liqun, ZHOU Guanglu. M-tensors and some applications [J]. SIAM Journal on Matrix Analysis and Applications, 2014, 35(2): 437-452.

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四川文理学院学报
2022年 第5期

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