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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (5): 709-718.doi: 10.3969/j.issn.1005-3085.2015.05.009

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$\gamma$-链对角占优矩阵与$H$-矩阵的判定

薛  媛,   刘建州   

  1. 湘潭大学数学与计算科学学院，湘潭  411105
  • 收稿日期:2013-11-28 接受日期:2014-05-19 出版日期:2015-10-15 发布日期:2015-12-15
  • 基金资助:
    国家自然科学基金重大研究计划重点支持项目 (91430213)；国家自然科学基金 (11471279)；长江学者和创新团队发展计划 (IRT1179)；湖南省自然科学基金 (2015JJ2134)；湖南省教育厅重点项目 (12A137)；湖南省研究生科研创新项目 (CX2014B254).

A Set of New Criterion for Judging Nonsingular $H$-matrices

XUE Yuan,   LIU Jian-zhou   

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105
  • Received:2013-11-28 Accepted:2014-05-19 Online:2015-10-15 Published:2015-12-15
  • Supported by:
    The National Natural Science Foundation for Major Research Plan Key Support Project of China (91430213); the National Natural Science Foundation of China (11471279); the Program for Changjiang Scholars and Innovative Research Team in University of China (IRT1179); the Natural Science Foundation of Hunan Province (2015JJ2134); the Key Project of Education Department of Hunan Province (12A137); the Innovation Foundation for Postgraduate of Hunan Province (CX2014B254).

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摘要： 非奇异$H$-矩阵作为一类特殊的矩阵，在计算数学、矩阵理论、经济数学、控制理论等领域有着非常广泛的应用．本文根据$M$-矩阵和$\gamma$-链对角占优矩阵的特殊性质，通过构造正对角矩阵以及细分矩阵指标集的方法，利用特殊的不等式和不等式的放缩技巧，给出了几个判别非奇异$H$-矩阵的新条件，推广了近期的一些结果，最后给出相应的数值例子来说明判别条件的有效性．

关键词: $H$-矩阵, 对角占优矩阵, 严格$\gamma$-链对角占优矩阵

Abstract:

Nonsingular $H$-matrix is a special class of matrices which has wide applications in computational mathematics, matrix theory, economic mathematics and control theory. In this paper, according to the special properties of $M$-matrices and $\gamma$-chain diagonally dominant matrices, and constructing positive diagonal matrices and subdividing the index set of matrices, we obtain several new conditions for judging $H$-matrices by applying some special inequalities and inequality techniques. The criteria extend some of the recent results, and the numerical examples illustrate the effectiveness of the theoretical results.

Key words: $H$-matrix, diagonally dominant matrix, strictly $\gamma$-chain diagonally dominant matrix

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