期刊文献+

一类线性方程组解的条件数估计 被引量:2

The condition number estimation for a class of linear systems
在线阅读 下载PDF
导出
摘要 利用矩阵范数的性质,给出了一类特殊线性方程组条件数估计,这有助于判别方程组解的灵敏度. In this paper, by the nature of matrix norm, we give the estimation of spectral norm condition number of the linear systems. The estimation can be used to measure the sensitivity of the solution of linear systems.
出处 《南京信息工程大学学报(自然科学版)》 CAS 2011年第2期190-192,共3页 Journal of Nanjing University of Information Science & Technology(Natural Science Edition)
基金 国家自然科学基金(40975037)
关键词 条件数 线性方程组 谱范数 谱半径 condition number linear systems spectral norm spectral radius
  • 相关文献

参考文献7

  • 1Higham D J. Condition numbers and their condition numbers [ J ]. Linear Algebra Appl, 1995,214 : 193-213.
  • 2Geurts A J. A contribution to the theory of condition[ J ]. Numerische Mathematik, 1952,39 ( 1 ) : 85-96.
  • 3Demmel J W. On condition numbers and the distance to the nearest ill-posed problem [ J ]. Numerische Mathematik, 1987,51 ( 3 ) :251-289.
  • 4杨兴东,黄卫红.Sylvester与Lyapunov方程向后误差分析[J].系统科学与数学,2008,28(5):524-534. 被引量:3
  • 5杨兴东,戴华.矩阵方程A^TXA=D的条件数与向后扰动分析[J].应用数学学报,2007,30(6):1086-1096. 被引量:7
  • 6Wei Y M, Zhang N M. Condition number related with generalized inverse AT,S(2)and constrained linear systems [ J ]. Journal of Computational and Applied Mathematics, 2003,157( 1 ) :57-72.
  • 7Marshall A W, Olkin I. Inequalities:Theory of majorization and its applications [ M ]. New York: Academic Press, 1979.

二级参考文献13

  • 1邓远北,胡锡炎.一类广义Sylvester方程的反对称最小二乘解及其最佳逼近[J].系统科学与数学,2004,24(3):382-388. 被引量:6
  • 2张庆灵.广义系统结构稳定性判别的李亚普诺夫方法[J].系统科学与数学,1994,14(2):117-120. 被引量:51
  • 3Wang B Y and Zang F Z. Schur complements and matrix inequalities of Hadamard products. Linear and Multilinear Algebra., 1997, 43: 315-326.
  • 4Zietak K. The chebyshev solution of the linear matrix equation AX + YB = C. Numer. Math., 1985, 46: 455-478.
  • 5Winuer H K. Consistency of a pair of generalized Sylvester equation. IEEE Trans. Automat. Contr., 1994, 39: 1014-1017.
  • 6Lancaster P. Explicit solutions of linear matrix equations. SIAM REV., 1970, 12: 544-566.
  • 7Higham N J. Perturbation theory and backward error for AX-XB = C. BIT., 1993, 33: 124-136.
  • 8Bo Kagstrom. A perturbation analysis of the generalized Sylvester matrix equation. SIAM J. Matrix Anal. Appl., 1994, 15(4): 1045-1060.
  • 9Wang B Y and Zang F Z. Trace and eigenvalue inequalities for ordinary and Hadamard product of positive semidefinite Hermitian matrices. SIAM J. Matrix Anal. Appl., 1995, 16(4): 1173-1183.
  • 10Horn Roger A and Johnson Charles R. Topics in Matrix Analysis. Cambridge, England: Cambridge University Press, 1991, 239-293.

共引文献8

同被引文献5

引证文献2

二级引证文献1

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部