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矩阵方程X^s+A~*X^(-t)A=I的Hermite正定解注记

A NOTE ON THE HERMITIAN POSITIVE DEFINITE SOLUTIONS OF THE MATRIX EQUATION X^s+A~*X^(-t)A=I
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摘要 考虑非线性矩阵方程Xs+A*X-tA=I,其中A是n阶非奇异复矩阵,I是n阶单位矩阵.讨论了该矩阵方程Hermite正定解的特性,改进了以往相应的结论. The Hermitian positive definite solutions of the matrix equation Xs＋A＊X-tA=I are studied,where I is the n×n identity matrix and A is a n×n non-singular complex matrix.Properties of the Hermitian positive definite solutions are investigated,which improves some existing results.
作者 周裕中 林利云
机构地区 华南农业大学理学院数学系
出处 《华南师范大学学报（自然科学版）》 CAS 北大核心 2010年第3期4-6,10,共4页 Journal of South China Normal University(Natural Science Edition)
基金 国家自然科学基金资助项目(10771076) 广东省自然科学基金资助项目(07006700)
关键词 矩阵方程 谱范数 FROBENIUS范数 matrix equation spectral norm Frobenius norm
分类号 O241.1 [理学—计算数学]
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参考文献8

  • 1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
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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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  • 6Sun J.G., Xu S.F., Perturbation analysis of the maximal solution of the matrix equation X + A^*X^-1A = P.II, Linear Algebra Appl., 362 (2003), 211-228.
  • 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18

华南师范大学学报（自然科学版）
2010年 第3期

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