期刊文献+

矩阵方程X-A~*X^(-1)A=Q的Hermite正定解及其扰动分析冰 被引量:6

THE HERMITIAN POSITIVE DEFINITE SOLUTION AND ITS PERTURBATION ANALYSIS FOR THE MATRIX EQUATION X-A~*X^(-1)A=Q
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摘要 考虑非线性矩阵方程X-A~*X^(-1)A=Q,其中A是n阶复矩阵,Q是n阶Hermite正定解,A~*是矩阵A的共轭转置.本文证明了此方程存在唯一的正定解,并推导出此正定解的扰动边界和条件数的显式表达式.以上结果用数值例子加以说明. Consider the nonlinear matrix equation X-A*x^-1A=Q, where A, Q are n ×n complex matrices with Q Hermitian positive definite and A* denotes the conjugate transpose of a matrix A. This paper shows there exists a unique positive definite solution to the equation. The perturbation bounds for the Hermitian positive definite solution to the matrix equation are derived, explicit expressions of the condition number for the Hermitian positive definite solution are obtained and the backward error of an approximate solution to the Hermitian positive definite solution is evaluated. The results are illustrated by numerical examples.
作者 李静 张玉海
出处 《计算数学》 CSCD 北大核心 2008年第2期129-142,共14页 Mathematica Numerica Sinica
基金 山东大学威海分校青年成长基金(z200608)
关键词 矩阵方程 正定解 扰动边界 条件数 matrix equation, positive definite solution, perturbation bound, condition number
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参考文献11

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同被引文献24

  • 1张玉海.非线性矩阵方程X+A~*X^qA=I(q>0)Hermite正定解的存在性[J].高等学校计算数学学报,2005,27(S1):110-113. 被引量:3
  • 2李静,张玉海.矩阵方程X-A*X^(-q)A=Q当q>1时的Hermite正定解[J].工程数学学报,2005,22(4):679-686. 被引量:11
  • 3陈小山,黎稳.关于矩阵方程X+A~*X^(-1)A=P的解及其扰动分析[J].计算数学,2005,27(3):303-310. 被引量:19
  • 4Jing L, Yuhai Zhang. Perturbation analysis of the matrix equation [J].Linear Algebra and Its Appl. 2009,431(9): 1489-1501.
  • 5Hasanov V I.Positive definite solutions of the matrix equations X + AtX-qA=Q [J].Linear Algebra and Its Appl.2005,404( 15): 166-182.
  • 6Lee H, et al. Invariant metrics, contractions and nonlinear matrix equations[J].Nonlinearity, 2008,21 (4):857-878.
  • 7André C.M Ran,Martine C.B Reurings.A nonlinear matrix equation connected to interpolation theory[J].Linear Algebra and Its Applications.2003
  • 8Zhao Wenling, Li Hongkui, Liu Xueting, Xu Fuyi. Necessary and sufficient conditions for the ex- istence of a Hermitian positive definite solution of a type of nonlinear matrix equations [J]. Math. Prob. Engin., 2009 (Article ID 672695): 1-13.
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  • 10Ran AndrC M, Reurings Martine C B. On the nonlinear matrix equation X + AHf(X)A = Q: solutions and perturbation theory [J]. Linear Alg. Appl., 2002, 346(1): 15- 26.

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