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关于算子方程X+A~*X^(-t)A=Q的正算子解的研究 被引量：7

Studies on the Positive Operator Solutions to Operator Equations X+A~*X^(-t)A = Q
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摘要 该文研究算子方程X+A~*X^(-t)A=Q的正算子解的问题,给出了算子方程X+ A~*X^(-t)A=Q有正算子解的一些必要条件,同时也给出了该算子方程有正算子解的充分必要条件. In this paper, the necessary conditions for the existence of positive operator solutions of the operator equation X ＋ A^＊X^-tA = Q are established. A sufficient and necessary condition for the existence of positive operator solutions for X ＋ A^＊X^-tA = Q is also derived.
作者 杨凯凡 杜鸿科
机构地区 陕西理工学院数学系 陕西师范大学数学与信息科学学院
出处 《数学物理学报（A辑）》 CSCD 北大核心 2009年第2期359-364,共6页 Acta Mathematica Scientia
基金 国家自然科学基金(10871224)资助
关键词 算子方程 谱 谱半径 正算子. Operator equation Spectrum Spectral radius Positive operator.
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献7

  • 1Ramadan Mohamed A, E1-Danaf Talaat S, EI-Shazly Naglaa M. Iterative positive definite solutions of the two nonlinear matrix equations X ± A*X-2A = I. Applied Mathematics and Computation, 2005, 164: 189-200
  • 2Conway J B. A Course in Operator Theory. Rhode Island: American Mathematical Society Providence, 2000:25-26
  • 3EI-Sayed Salah M, Petkov Milko G. Iterative methods for nonlinear matrix equations X + A*X-αA = I. Linear Algebra Appl, 2005, 403:45-52
  • 4Hasanov Vejdi I. Positive definite solutions of the matrix equations X ± A*X-qA = Q. Linear Algebra Appl, 2005, 404:166-182
  • 5Ran A C M, Reurings Martine C B. On the nonlinear equation X + A*F(X).A = Q: solutions and perturbation theory. Linear Algebra Appl, 2002, 346:15-26
  • 6E1-Sayed S M, Ran A C M. On an iteration method for solving a class of nonlinear matrix equations. SIAM J Matrix Anal Appl, 2001, 23:632-645
  • 7Ran A C M, Reurings M C B. The symmetric linear matrix equation. Electron J Linear Algebra, 2002, 9: 93-107

同被引文献45

  • 1杨凯凡.算子方程X+A~* X^(-2) A=Q有正算子解的必要条件[J].宝鸡文理学院学报（自然科学版）,2006,26(3):173-175. 被引量：2
  • 2Mohamed A Ramadan, Talaat S, El-Danaf, Naglaa M, El-Shazly. Iterative positive definite solutions of the two nonlinear matrix equations X±A^*X^-2A =I[J]. Applied Mathematics and Computation, 2005, 164: 189-200.
  • 3Salah M, El-Sayed, Milko G. Petkov. Iterative methods for nonlinear matrix equations X + A^*X^-αA = I[J]. Lincar Algebra Appl, 2005, 403: 45-52.
  • 4Ran A C M and Reurings M C B. The symmetric linear matrix equation[J]. Electron J Linear Algebra, 2002(9): 93-107.
  • 5Conway J B. A Course in Functional Analysis[M]. Springer-Verlag, 1990.
  • 6Gustafson K E, Rao D K M. Numerical Range[M]. New York: Springer-Verlag, 1997.
  • 7Engwerda J C. On the existence of a positive definite solution of the matrix equation X+A^TX^- 1A = I[J]. Linear Algebra Appl, 1993(194): 91-108.
  • 8Mohamed A. Ramadan, Talaat S. EI-Danaf, Naglaa M. EI-Shazly, Iterative positive definite solutions of the two nonlinear matrix equations X±A^*X^-2A = I[J]. Applied Mathematics and Computation, 2005(164): 189-200.
  • 9Salah M. E1-Sayed, Milko G. Petkov, Iterative methods for nonlinear matrix equations X+A^*X^-αA= I[J]. Linear Algebra Appl, 2005(403): 45-52.
  • 10Ran A C M and Reurings M C B. The symmetric linear matrix equation[J]. Electron J Linear Algebra, 2002(9): 93-107.

引证文献7

二级引证文献13

数学物理学报（A辑）
2009年 第2期

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