数值计算与计算机应用
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数值计算与计算机应用  2015, Vol. 36 Issue (3): 215-224    DOI:
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H-张量的判定及其应用
王峰, 孙德淑
贵州民族大学理学院, 贵阳 550025
CRITERIA FOR H-TENSORS AND AN APPLICATION
Wang Feng, Sun Deshu
College of Science, Guizhou Minzu University, Guiyang 550025, China
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摘要 H-张量在科学计算和工程应用中具有重要的作用,但在实际中要判定一给定张量为H-张量是不容易的.本文通过构造不同的正对角阵和运用不等式的放缩方法,给出了H-张量的一组实用性新判定方法.作为应用,给出了偶数阶实对称张量正定性判定的新条件.数值算例表明了结果的有效性.
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关键词H-张量   实对称张量   正定性   不可约     
AbstractH-tensors have wide applications in the scientific computation and the applications in engineering, but it is not easy to determine whether a given tensor is an H-tensor or not in practice. In this paper, we give some practical criteria for H-tensors 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 are given. Advantages of results obtained are illustrated by numerical examples.
Key wordsH-tensors   real symmetric tensors   positive definiteness   irreducible   
收稿日期: 2015-07-24;
基金资助:

国家自然科学基金(11501141,11361074);贵州省科学技术基金([2015]2073);贵州省科技厅联合基金([2015]7206);贵州省教育厅自然科学基金([2015]420);贵州民族大学科研基金(15XRY004).

引用本文:   
. H-张量的判定及其应用[J]. 数值计算与计算机应用, 2015, 36(3): 215-224.
. CRITERIA FOR H-TENSORS AND AN APPLICATION[J]. Journal of Numerical Methods and Computer Applicat, 2015, 36(3): 215-224.
 
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