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严格对角占优M-矩阵的‖A^(-1)‖_∞上界的一个新的估计式(英文) 被引量：10

A new upper bound for ‖A^(-1)‖_∞ of a strictly diagonally dominant M-matrix
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摘要 设A为严格对角占优的M-矩阵,给出了‖A-1‖∞的一个新的上界估计式,进而给出了A的最小特征值q(A)下界的一个估计式,这些新的估计式改进了已有的结果。 Let A be a real strictly diagonally dominant M-matrix.A new upper bound for ‖A-1‖∞ is given.Also,a lower bound of the smallest eigenvalue q（A） of A is presented,which improves the results in the literature.
作者 王亚强 李耀堂 孙小军 李艳艳
机构地区 云南大学数学与统计学院数学系 宝鸡文理学院数学系
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2010年第4期43-47,共5页 Journal of Shandong University(Natural Science)
基金 Supported by the Natural Science Foundation of China(No.10961027) the Key Foundation of Baoji University of Arts and Sciences(No.ZK0931)
关键词 对角占优 M-矩阵 逆M-矩阵 diagonal dominance M-matrix inverse M-matrix
分类号 O151.21 [理学—基础数学]
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参考文献11

  • 1HORN R, JOHNSON C R, Topics in matrix analysis[M]. New York:Cambridge University Press, 1991.
  • 2JOHNSON C R. A Hadamard product involving M-matrix[J]. Linear and Multilintar Algebra, 1997, 4:261-264.
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  • 5CHENG G H, HUANG T Z. An upper bound for Ⅱ A^-1 Ⅱ - of strictly diagonally dominant M-matrices[J]. Linear Algebra Appl, 2007, 426:667-673.
  • 6WANG P. An upper bound for Ⅱ A^-1 Ⅱ∞ of strictly diagonally dominant M-matrices[J]. Linear Algebra Appl, 2009, 431 : 511-517.
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同被引文献56

  • 1SHIVAKUMAR P N, CHEW K H. A sufficient condition for nonvanishing of determinants [ J ]. Proc Amer Math Soc, 1974,43 (1) :63-66.
  • 2CHENG Guang-hui, HUANG Ting-zhu. An upper bound for ‖A^-1‖∞ of strictly diagonally dominant M - matrices [ J ]. Linear Algebra and its Applications,2007,426 (2/3) :667 - 673.
  • 3陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2000.130.
  • 4VARAHJ M.A lower bound for the smallest singular value of a matrix [ J ] .Linear Algebra Appl, 1975,11:3-5.
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  • 6LI Y T,CHEN F B,WANG D F.New lower bounds on eigenvalue of the Hadamard product of an M-matrix and its inverse [ J ].Linear Algebra Appl, 2009,430:1 423-1 431.
  • 7NENAD M.Upper bounds for the infinity norm of the inverse of SDD and S-SDD matrices[ J] .Journal of Computational and Applied Mathematics, 2007,206: 666-678.
  • 8LI W.The infinity norm bound for the inverse of nonsingular diagonal dominant matrices [ J ]. Applied Mathematics Letters, 2008,21 : 258-263.
  • 9CHENG G L, HUANG T Z.An upper bound for A-1of strictly diagonally dominant M-matrices[ J] .Linear Algebra Appl, 2007,426:667-673.
  • 10WANG P. An upper bound for A- 1 of strictly diagonally dominant M- matriees [ J ]. Linear Algebra Appl, 2009,431 : 511 - 517.

引证文献10

二级引证文献48

山东大学学报（理学版）
2010年 第4期

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