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矩阵方程X+A~* X^(-p)A=I当p>0时的准最大解的条件数

Condition number of the quasi-maximal solution to a matrix equation X+A~* X^(-p)A=I when p>0
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摘要 讨论了非线性矩阵方程X+A*X-pA=I在p>0时的准最大解的条件数,并且推导出了此条件数的显式表达式。 Consider the nonlinear matrix equation X＋A^＊ X^-P A=I（p 〉 0）, where A is n x n complex matrix and A^＊ denotes the conjugate transpose of a matrix A. The explicit expressions of the condition number of the quasi-maximal solution were obtained.
作者 李静 张玉海
机构地区 山东大学威海分校应用数学系 山东大学数学与系统科学学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2007年第12期90-94,共5页 Journal of Shandong University(Natural Science)
基金 山东大学威海分校青年成长基金(z200608)
关键词 矩阵方程 条件数 准最大解 matrix equation condition number quasi-maximal solution
分类号 O241.7 [理学—计算数学]
  • 相关文献

参考文献12

  • 1IVANOV I G, El-Sayed S M. Properties of positive definite solution of the equation X + A^*X^-2A = I [ J]. Linear Algebra Appl, 1998, 279: 303-316.
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  • 3ZHANG Y H. On Hermitian positive definite solutions of matrix equation X + A ^* X^-2A = I[J]. Linear Algebra Appl, 2003, 372:295- 304.
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  • 6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
  • 7HASANOV V I, IVANOV I G. On two perturbation estimates of the extreme solutions to the equations X + A ^· X^-1 A = Q[J]. Linear Algebra Appl, 2006, 413 : 81-92.
  • 8王进芳,张玉海,朱本仁.矩阵方程X+A~*X^(-q)A=I(q>0)的Hermite正定解[J].计算数学,2004,26(1):61-72. 被引量：28
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二级参考文献9

  • 1Anderson W.N., Morley T.D., Trapp G.E., Positive solutions to X = A-BX^-1B*, Linear Algebra Appl., 134(1990), 53-62.
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  • 3Engwerda J.C., Ran A.C.M., Rijkeboer A.L., Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X + A^*X^-1A = I, Linear Algebra Appl., 186(1993), 255-275.
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  • 7Liu X.G., Gao H., On the positive definite solutions of the matrix equations X^s±A^T X^-tA = In, Linear Algebra Appl., 368 (2003), 83-97.
  • 8Ran A.C.M., Reurings M.C.B., On the nonlinear matrix equation X + A^*F(X)A = Q:solutions and perturbation theory, Linear Algebra Appl., 346 (2002), 15-26.
  • 9Zhang Yuhai, On Hermitian positive definite solutions of matrix equation X + A^*X^-2A =I, Linear Algebra Appl., 326 (2001), 27-44.

共引文献43

山东大学学报（理学版）
2007年 第12期

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