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关于算子方程X-A~*X^(-t)A=I 被引量：3

On the Operator equation X-A~*X^(-t)A=I
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摘要 文章给出了算子方程X-A*X-tA=I有正算子解的一些必要条件,并且采用迭代的方法得到了当t=2m(m为正整数)时算子方程X-A*X-tA=I的正算子解存在的充分条件。。 In this paper, the necessary conditions for the existence ot positive operator somt ons. of the operator equation X-A^＊X^-tA=I are established. Effective iterative methods to obtain the sufficient conditions for the existence of positive operator solutions for X-A^＊X^-tA=I are derived when t=2^m, where m is a positive integer.
作者 杨凯凡 杜鸿科
机构地区 陕西师范大学数学与信息科学学院
出处 《云南师范大学学报（自然科学版）》 2006年第1期1-5,共5页 Journal of Yunnan Normal University:Natural Sciences Edition
基金 国家自然科学基金资助项目(19971056)
关键词 算子方程 正算子 operator equation positive operator
分类号 O177.91 [理学—基础数学]
  • 相关文献

参考文献7

  • 1J. B. Conway. A Course in Functional Analysis[M]. Springer-Verlag, 1990.
  • 2J. Murphy. Gerard, C* -Algebra and Operator Theory[M]. New York, 1990.
  • 3J. B. Conway. A Course in Operator Theory, American Mathematical Society Providence, Rhode Island, 2000.
  • 4Mohamed A. Ramadan, Talaat S. E1-Danaf, Naglaa M. E1-Shazly. herative positive definite solutions of the two nonlinear matrix equations X+A* X-2A=I[J]. Applied Mathematics and Computation, 164(2005), 189-200.
  • 5Sa ah M. E1-Sayed, Milko G. Petkov. Iterative methods for nonlinear matrix equations X+A* X^-*A =I[J]. Linear Algebra Appl. 403(2005),45-52.
  • 6S. M. E1-Sayed,A. C. M. Ran. On an Iteration Method for Solving a Class of Nonlinear Matrix Equations[J]. SIAM J. Matrix Anal. Appl. 23(2001) ,632-645.
  • 7A. C. M. Ran and M. C. B. Reurings. The symmetric linear matrix equation[J]. Eletron J. Linear Algebra, 9(2002), 93-107.

同被引文献12

  • 1ZHANG Y H. On Hermitian positive definite solutions of ma- trix equation X+A* X-ZA= I [J]. Linear Algebra Appl, 2003,372 : 295-304.
  • 2RAMADAN M A, EL-DANAF T S, EI.-SHAZLY N M. hera- tire positive definite solutions of two nonlinear matrix equa- tions X±A · X-ZA= Ⅰ [J]. Applied Mathematics and Compu- tation, 2005,164 : 189-200.
  • 3EI:SAYED S M,PETKOV M G. lterative methods for nonlin- ear matrix equations X+A" X-αA = Ⅰ [J]. Linear Algebra Appl, 2005,403 : 45-52.
  • 4CONWAY J B. A Course in Functional Analysis[M]. New York: Springer-Verlag, 1990.
  • 5GERARD J NL C*-Algebra and Operator Theory [M]. New York: Inc. Academic Press, 1990.
  • 6J.B. Conway, A Course in Functional Analysis[ M] , Springer - Verlag, 1990.
  • 7J. B. Conway. A Course in Operator Theory[ M ] , American Mathematical Society Providence, Rhode Island,2000.
  • 8Gerard J M. C^* -Algebra and Operator Theory[M]. New York: Inc. Academic Press,1990.
  • 9Salah M. El - Sayed, Milko G. Petkov, Iterative methods for nonlinear matrix equations X + A^*X^-αA =I[ J ] , Linear Algebra Appl. 403 (2005) 45-52.
  • 10S.M. El - Sayed, A. C. M. Ran, On an Iteration Method for Solving a Class of Nonlinear Matrix Equations[J] ; SIAM J. Matrix Anal. Appl. 23(2001) 632-645.

引证文献3

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云南师范大学学报（自然科学版）
2006年 第1期

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