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严格对角占优M-矩阵A的‖A^(-1)‖_∞上界序列 被引量：2

The Sequence of Upper Bounds for the ‖A^(-1)‖_∞ of Strictly Diagonally Dominant M-matrices A
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摘要 借助行严格对角占M-优矩阵的逆矩阵元素的上界序列,得到了‖A-1‖∞收敛的递减上界序列,A的最小特征值q(A)收敛的递增的下界序列.从理论上证明了本文结果的优越性,通过数值例子进一步说明了可行性和有效性. By using the upper sequence of the elements of inverse matrix of strictly diagonally dominant Mmatrix,a decreasing sequence of upper bounds for convergence of ‖ A- 1‖∞was obtained,the minimum eigenvalue q（ A） of A the increasing sequence of lower bounds for convergence. Furthermore,the superiority of the results was theoretically proved. A numerical example feasibility and effectiveness were illustrated.
作者 蒋建新 李艳艳
机构地区 文山学院数学学院
出处 《吉林师范大学学报（自然科学版）》 2015年第4期60-63,共4页 Journal of Jilin Normal University:Natural Science Edition
基金 国家自然科学基金项目(11361074) 云南省教育厅科学研究基金项目(2013Y585) 文山学院重点学科数学建设项目(12WSXK01)
关键词 对角占优矩阵 M-矩阵 矩阵的无穷大范数 上界 最小特征值 Diagonal dominance matrix M-matrix Infinity norms of matrices Upper bound Minimum eigenvalue
分类号 O151.21 [理学—基础数学]
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参考文献8

  • 1陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2000.130.
  • 2P. N. Shivakumar, K. H. Chew. A sufficient condition for nonvanishing of determinants [ J ]. Proc Amer. Math. Soc. , 1974,43:63 - 66.
  • 3G. H. C heng,T. Z. Huang. An upper bound for II A -1 II - of strictly diagonally dominant M-matrices [ J ]. Linear Algebra Appl,2009,43:511 - 517.
  • 4王亚强,李耀堂,孙小军,李艳艳.严格对角占优M-矩阵的‖A^(-1)‖_∞上界的一个新的估计式(英文)[J].山东大学学报（理学版）,2010,45(4):43-47. 被引量：10
  • 5P. Wang. An upper bound for II A -1 I I of strictly diagonally dominant M-matrix [ J ]. Linear Algebra Appl,2009 ,431:511 -517.
  • 6P. N. Shivakumar, J. Williams, Y. Qiang, et al. On two-sided bounds related to weakly diagonally dominant M-matrix with application to digital circuit dynamics [ J ]. SIAM J Matrix Anal Appl, 1996,17 (2) :298 - 312.
  • 7R. Horn, C. R. Johnson. Topics in matrix analysis [ M ]. New York:Cambridge University Press, 1991.
  • 8C. R. Johnson. A Hadamard product involving-matrix [ J ]. Linear and Multilinear Algebra, 1997,4:261 - 264.

二级参考文献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.
  • 3FIEDLER M, JOHNSON C R, MARKHAM T L, et al. A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix[J]. Linear Algebra Appl, 1988, 102:1-8.
  • 4SHIVAKUMAR P N, WILLIAMS Joseph, YE Qiang, et al. On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital circuit dynamics [J]. SIAM J Matrix Anal Appl, 1996, 17 (2) :298-312.
  • 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.
  • 7BERMAN A, PLEMMONS R J. Nonnegative matrices in the mathematical sciences [M]. 3rd ed. New York: Academic Press, 1994.
  • 8SHIVAKUMAR P N, CHEW K H. A sufficient condition for nonvanishing of determinants[J]. Proc Amer Math Soc, 1974, 43:63-66.
  • 9LI 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 : 1423-1431.
  • 10VARGA R S, On diagonal dominance arguments for bounding Ⅱ A^-1 Ⅱ∞ [J]. Linear Algebra Appl, 1976, 14:211-217.

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吉林师范大学学报（自然科学版）
2015年 第4期

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