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严格对角占优M-矩阵A的|A^(-1)|_∞上界估计式的改进 被引量：20

The improved upper bound estimation of |A^(-1)|_∞ for strictly diagonally dominant M-matrices
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摘要 利用严格对角占优M-矩阵A的逆矩阵A-1的非主对角元素上界的估计式,给出了|A(-1)|∞上界估计式的改进.证明了所得估计式改进了几个现有文献的结果,并用数值算例进行了说明. Several improved upper bounds of ｜A^-1｜_∞ are given for strictly diagonally dominant M-matrixby using the upper bound estimations of non main diagonal elements for the inverse matrix A^-1 of matrix A, and we prove that the estimators improve some results of existing literatures, and it is illustrated with numerical examples.
作者 李艳艳 蒋建新 李耀堂
机构地区 文山学院数学学院 云南大学数学与统计学院
出处 《云南大学学报（自然科学版）》 CAS CSCD 北大核心 2015年第1期5-8,共4页 Journal of Yunnan University(Natural Sciences Edition)
基金 国家自然科学基金(11261049) 云南省教育厅科学研究基金(2013Y585) 文山学院重点学科数学建设项目(12WSXK01)
关键词 弱链对角占优 严格对角占优 M-矩阵 范数 上界 weakly chained diagonally dominant matrix strictly diagonally dominant matrix M- matrix Norm upper bound
分类号 O151.21 [理学—基础数学]
  • 相关文献

参考文献12

  • 1VARAHJ M.A lower bound for the smallest singular value of a matrix [ J ] .Linear Algebra Appl, 1975,11:3-5.
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  • 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.
  • 8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
  • 9杨晓英,曾宝国,朱清溢,刘新.严格对角占优M-矩阵A的‖A^(-1)‖_∞上界的新估计式[J].湖南师范大学自然科学学报,2014,37(3):91-94. 被引量：8
  • 10HUANG T Z, ZHU Y. Estimation of for weakly chained diagonally dominant M- matrix [ J ]. Linear Algebra Appl. 2010,431 : 670-677.

二级参考文献45

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  • 7CHENG 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.
  • 8WANG 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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共引文献26

同被引文献69

  • 1Varga R S. Matrix iterative analysis [M]. Berlin: Springer, 2000.
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  • 4Shivakumar P N, Williams J J, Ye Q, Marinov C.A. On two-sided bounds related to weakly diago- nally dominant M-matrices with application to digital circuit dynamics [J]. SIAM J. Matrix Anal. Appl., 1996, 17: 298-312.
  • 5Cheng G H, Huang T Z. An upper bound for /A-1 of strictly diagonally dominant M-matrices [J]. Linear Algebra Appl., 2007, 426: 667-673.
  • 6Wang P. An upper bound for A-1 o of strictly diagonally dominant M-matrices [J]. Linear Algebra Appl., 2009, 431: 511-517.
  • 7Huang T Z, Zhu Y. Estimation of IIA-111 for weakly chained diagonally dominant 2l-matrices [J]. Linear Algebra Appl., 2010, 432: 670-677.
  • 8Varga R S. Matrix herative Analysis ~M~. 2nd ed. Berlin: Springe>Verlag, 2000.
  • 9Varah ] M. A Lower Bound {or the Smallest Singular Value o{ a Matrix ~J~. Linear Algebra and Its Applications, 1975, 11(1): 3-5.
  • 10Shivakumar P N, Williams J J, YE Qiang, et al. On Two-Sided Bounds Related to Weakly Diagonally Dominant M-Matrices with Application to Digital Circuit Dynamics ~J~. SIAM Journal on Matrix Analysis and Applications, 1996, 17(2): 298-312.

引证文献20

二级引证文献66

云南大学学报（自然科学版）
2015年 第1期

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