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严格对角占优M-矩阵A的‖A^(-1)‖_∞上界的新估计式 被引量：8

New Upper Bound for ‖A^(-1)‖_∞ of Strictly Diagonally Dominant M-matrices
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摘要 针对严格对角占优M-矩阵A,利用矩阵元素,估计其逆矩阵元素的取值范围,进而给出‖A-1‖∞新的上界估计式,由此得到A的最小特征值下界的估计式.理论证明和算例分析表明新的上界估计式改进了一些已有结果. Let A be a real strictly diagonally dominant M-matrix.Using the element of M-matrix,the ranges for the elements of inverse matrix are given,and an upper bound for ‖A^-1‖∞is obtained.Furthermore,the lower bound of the smallest eigenvalue of A is presented.The given numerical example shows that these bounds improve several existing results.
作者 杨晓英 曾宝国 朱清溢 刘新
机构地区 四川信息职业技术学院基础教育部 四川信息职业技术学院电子工程系 电子科技大学物理电子学院
出处 《湖南师范大学自然科学学报》 CAS 北大核心 2014年第3期91-94,F0003,共5页 Journal of Natural Science of Hunan Normal University
基金 四川省产业技术研究与开发资金资助项目(2011XM065) 中央高校基本科研业务费专项资金资助项目(ZYGX2011YB020) 四川省教育厅自然科学研究基金资助项目(132B0393)
关键词 对角占优矩阵 M-矩阵 无穷大范数 上界 diagonally dominant matrix M-matrix infinity norm upper bound
分类号 O151.21 [理学—基础数学]
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参考文献12

  • 1SHIVAKUMAR P N,WILLIAMS J J,YE Q, et al. On two-sided bounds related to weakly diagonally dominant M-matrices withapplication to digital circuit dynamics[ J]. SIAM J Matrix Anal Appl, 1996,17(2) :298-312.
  • 2VARAH J M. A lower bound for the smallest singular value of a matrix[ J]. Linear Algebra Appl, 1975 ,11(1) :3-5.
  • 3CHENG G H,HUANG T Z. An upper bound for || A || w of strictly diagonally dominant M-matrices [J]. Linear Algebra Ap-pl, 2007,426(2/3) :667-673.
  • 4WANG P. An upper bound for || A _1 || w of strictly diagonally dominant M-matrices [J]. Linear Algebra Appl, 2009,431 (5/7):511-517.
  • 5HUANG T Z,ZHU Y. Estimation of || A _1 || . for weakly chained diagonally dominant M-matrices[ J]. Linear Algebra Appl,2010,43(2/3) :670-677.
  • 6VARGA R S. On diagonal dominance arguments for bounding || A _t || . [ J]. Linear Algebra Appl, 1976,17(3) :211-217.
  • 7LI W. The infinity norm bound for the inverse of nonsingular diagonal dominant matrices[ J]. Appl Math Lett, 2008 ,21 ( 3 ):258-263.
  • 8HORN R A, JOHNSON C R. Topics in matrix analysis[ M]. New York;Cambridge University Press, 1991 : 113-115.
  • 9JOHNSON C R. A Hadamard product involving M-matrices[ J], Linear Multilinear Algebra, 1977,4(4) ;261-264.
  • 10FIEDLER M, JOHNSON C R, MARKHAM T L, ei al. A trace inequality for M-matrices and the symmetrizability of a real ma-trix by a positive diagonal matrix[ J]. Linear Algebra Appl, 1985,71 (11) :81-94.

同被引文献49

  • 1VARAHJ M.A lower bound for the smallest singular value of a matrix [ J ] .Linear Algebra Appl, 1975,11:3-5.
  • 2LI W. On Nekrasov matrices [ J ]. Linear Algebra Appl, 1998,28 : 187-86.
  • 3LI 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.
  • 4NENAD 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.
  • 5LI W.The infinity norm bound for the inverse of nonsingular diagonal dominant matrices [ J ]. Applied Mathematics Letters, 2008,21 : 258-263.
  • 6CHENG G L, HUANG T Z.An upper bound for A-1of strictly diagonally dominant M-matrices[ J] .Linear Algebra Appl, 2007,426:667-673.
  • 7WANG P. An upper bound for A- 1 of strictly diagonally dominant M- matriees [ J ]. Linear Algebra Appl, 2009,431 : 511 - 517.
  • 8HUANG T Z, ZHU Y. Estimation of for weakly chained diagonally dominant M- matrix [ J ]. Linear Algebra Appl. 2010,431 : 670-677.
  • 9CHENG G H, HUANG T Z. An Upper Bound for || A-1||∞ of Strictly Diagonally Dominant M-Matrices[J]. Linear Alge- bra Appl, 2007, 426(S2/3): 667-673.
  • 10WEN L. The Infinity Norm Bound for the Inverse of Nonsingular Diagonal Dominant Matrices [J]. Applied Mathematics Letters, 2008, 21: 258-263.

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湖南师范大学自然科学学报
2014年 第3期

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