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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 (3): 416-424.doi: 10.3969/j.issn.1005-3085.2015.03.010

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非奇异$H$-矩阵的一组充分条件

李   玲,   徐   仲,   陆   全   

  1. 西北工业大学应用数学系，西安  710072
  • 收稿日期:2013-12-03 接受日期:2014-06-23 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (10802068).

Sufficient Conditions for Nonsingular $H$-matrices

LI Ling,   XU Zhong,   LU Quan   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072
  • Received:2013-12-03 Accepted:2014-06-23 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of China (10802068).

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摘要： 非奇异$H$-矩阵在数值线性代数的理论与应用中起着重要作用，因此研究非奇异$H$-矩阵的判定条件有着非常重要的理论价值．本文根据广义严格$\alpha$-链对角占优矩阵和广义严格$\alpha$-对角占优矩阵的性质，通过引入迭代因子，给出了一组非奇异$H$-矩阵新的迭代判定条件．该判定条件推广和改进了相关已有结果，丰富和完善了非奇异$H$-矩阵的理论，最后用数值算例说明了其有效性．

关键词: 广义严格$\alpha$-链对角占优矩阵, 广义严格$\alpha$-对角占优矩阵, 非奇异$H$-矩阵, 迭代因子

Abstract:

Nonsingular $H$-matrices play important roles in the theory and application of numerical linear algebra, therefore, it is very important for us to study the determinate conditions for a nonsingular $H$-matrix. In this paper, we present some sufficient conditions for nonsingular $H$-matrices according to the properties of generalized strictly $\alpha$-chain diagonally dominant matrices, generalized strictly $\alpha$-diagonally dominant matrices and by introducing the iteration factors. The proposed conditions improve some related results and the theory of nonsingular $H$-matrices is also enriched. Finally, the effectiveness of these sufficient conditions is illustrated with numerical examples.

Key words: generalized strictly $\alpha$-chain diagonally dominant matrix, generalized strictly $\alpha$-diagonally dominant matrix, nonsingular $H$-matrix, iteration factor

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