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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): 719-725.doi: 10.3969/j.issn.1005-3085.2015.05.010

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严格对角占优$M$-矩阵的逆矩阵的无穷大范数上界的估计

王   永   

  1. 临沂大学费县分校，临沂 273400
  • 收稿日期:2014-03-26 接受日期:2015-04-09 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 (71162005).

Estimation on Upper Bounds for the Infinity Norm of Inverse Matrix of Strictly Diagonally Dominant $M$-matrix

WANG Yong   

  1. Feixian College, Linyi University, Linyi 273400
  • Received:2014-03-26 Accepted:2015-04-09 Online:2015-10-15 Published:2015-12-15
  • Supported by:
    The National Natural Science Foundation of China (71162005).

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摘要： $M$-矩阵在数学物理、控制论、电力系统理论等领域具有重要的实际应用价值．近年来，关于严格对角占优$M$-矩阵的逆矩阵在无穷大范数下的上界估计已经成为研究的热点．本文首先引入一组新的记号，然后利用逆矩阵元素的估计式和代数运算方法，给出严格对角占优$M$-矩阵的逆矩阵无穷大范数新的上界估计式．理论分析和数值算例表明新估计式改进了现有的一些结果．

关键词: 对角占优, $M$-矩阵, 无穷大范数

Abstract:

$M$-matrix is applied widely in mathematical physics, cybernetics, electric system and so on. In recent years, the upper bound estimate on the infinity norm of inverse matrix of a strictly diagonally dominant $M$-matrix has become an important problem. Firstly, some new notations are introduced in this paper. Then, applying the range for the elements of inverse matrix and algebra methods, some new upper bounds for the infinity norm of inverse matrix of a strictly diagonally dominant $M$-matrix are obtained. Finally, the theory analysis and numerical results show that the new upper bound estimates improve some of the related results.

Key words: diagonal dominance, $M$-matrix, infinity norm

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