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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 ›› 2016, Vol. 33 ›› Issue (2): 163-174.doi: 10.3969/j.issn.1005-3085.2016.02.006

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非奇异$H$-矩阵的一组判定条件

崔静静,   陆  全,   徐  仲,  安晓虹   

  1. 西北工业大学应用数学系，西安 710072
  • 收稿日期:2014-07-08 接受日期:2014-12-30 出版日期:2016-04-15 发布日期:2016-05-15
  • 基金资助:
    国家自然科学基金 (10802068).

A Set of Determinate Conditions for Nonsingular $H$-matrices

CUI Jing-jing,   LU Quan,   XU Zhong,   AN Xiao-hong   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072
  • Received:2014-07-08 Accepted:2014-12-30 Online:2016-04-15 Published:2016-05-15
  • Supported by:
    The National Natural Science Foundation of China (10802068).

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摘要： 非奇异$H$-矩阵在计算方法、物理数学、生物学、矩阵论、控制理论等领域有着广泛的应用，如何有效地判定一个矩阵是否为非奇异$H$-矩阵，一直是人们关心的问题．本文利用矩阵指标集的$k$-级划分，给出了非奇异$H$-矩阵的一组判定条件，改进和推广了近期的相关结果，并用数值算例说明本文判定方法的有效性．

关键词: 非奇异$H$-矩阵, 对角占优矩阵, 不可约, 非零元素链

Abstract:

Nonsingular $H$-matrices has a wide range of applications in computational mathematics, physical mathematics, biology, matrix theory and control theory, etc. How to specify nonsingular $H$-matrices effectively has always been paid attention. In the paper, by applying $k$-partition of matrices index set, a set of determinate conditions for nonsingular $H$-matrices are given, which improve and generalize some recent related results. The effectiveness of these determinate conditions in this paper is illustrated with numerical examples.

Key words: nonsingular $H$-matrices, diagonally dominant matrix, irreducibility, nonzero elements chain

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