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齐次多项式正定性的判定准则 被引量：1

New Criteria for Identifying the Positive Definiteness of Multivariate Homogeneous Forms
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摘要 通过构造新的正对角因子,给出了H-张量新的判定不等式。给出了偶数阶实对称张量,即偶次齐次多项式正定性的新判别条件,并用数值例子表明了新结果的有效性。 Some practical conditions for H-tensors were studied by constructing different positive diagonal matrices and applying some techniques of inequalities.As an application,some sufficient conditions of the positive definiteness for an even-order real symmetric tensor were obtained.Advantages of results obtained were illustrated by numerical examples.
作者 孙德淑 吴念 柏冬健 王峰 SUN Deshu;WU Nian;BAI Dongjian;WANG Feng(College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 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 《郑州大学学报（理学版）》 CAS 北大核心 2021年第2期96-101,共6页 Journal of Zhengzhou University:Natural Science Edition
基金 国家自然科学基金项目(11861077) 贵州省科学技术基金项目(20181079,20191161) 贵州民族大学自然科学基金项目(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 H-tensors positive definiteness irreducible nonzero elements chain
分类号 O151.21 [理学—基础数学]
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  • 1QI Liqun. Eigenvalues of a real supersymetric tensor [J]. Journal of Symbolic Computation, 2005, 40(6): 1302-1324.
  • 2Kannana M R, Mondererb N S, Bermana A. Some properties of strong H-tensors and general H- tensors [J]. Linear Algebra and its Applications, 2015, 476: 42-55.
  • 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.
  • 4Kolda T G, Mayo J R. Shifted power method for computing tensor eigenpairs [J]. SIAM Journal on Matrix Analysis and Applications, 2011, 32(4): 1095-1124.
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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.
  • 8NI Qin, QI Liqun, WANG Fei. An eigenvalue method for the positive definiteness identification problem [J]. IEEE Transactions on Automatic Control, 2008, 53(5): 1096-1107.
  • 9NI Guyan, QI Liqun, WANG Fei, WANG Yiju. The degree of the E-characteristic polynomial of an even order tensor [J]. Journal of Mathematical Analysis and Applications, 2007, 329(2): 1218-1229.
  • 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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郑州大学学报（理学版）
2021年 第2期

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