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非线性算子方程X^(-1)+(AXA~*)^(1/t)=Q的正算子解的研究 被引量：1

Studies on the Positive Operator Solutions to Nonlinear Operator Equations X^(-1)+(AXA~*)^(1/t)=Q
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摘要 在无限维Hilbert空间上研究了算子方程X^(-1)+(AXA~*)^(1/t)=Q(t>1)的正算子解问题.通过构造有效的迭代序列,研究了算子方程正算子解存在的充要条件,给出了该方程有正算子解时各算子范数之间的关系以及解的范围,并用迭代的方法得到了方程的正算子解. In infinite demensional Hilbert space, the positive operator solutions to the oper- ator equation X^-1＋（AXA^＊）^1/t=Q（t 〉 1） is studied. The ralation of norm of the operators has been given when the operator equationthe has positive operator solutions. The necessary conditions and sufficient conditions for the existence of positive operator solutions to the oper- ator equation X^-1＋（AXA^＊）^1/t = Q are derived. An iterative method for finding the positive operator solutions is construsted.
作者 杨凯凡 邓方安 窦艳妮
机构地区 陕西理工学院数学与计算机科学学院 陕西师范大学数学与信息科学学院
出处 《数学的实践与认识》 北大核心 2015年第8期279-282,共4页 Mathematics in Practice and Theory
基金 国家自然科学基金(11301318 项目依托单位:陕西师范大学) 汉中市科技局项目(2013hzzx-40)
关键词 算子方程 正算子 迭代法 范数 operator equation positive operator iterative method norm
分类号 O177.1 [理学—基础数学]
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参考文献10

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  • 3杨凯凡.一类算子方程的正算子解的研究[J].数学的实践与认识,2010,40(16):160-165. 被引量：3
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二级参考文献14

  • 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
  • 2Ramadan 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
  • 3Conway J B. A Course in Operator Theory. Rhode Island: American Mathematical Society Providence, 2000:25-26
  • 4EI-Sayed Salah M, Petkov Milko G. Iterative methods for nonlinear matrix equations X + A*X-αA = I. Linear Algebra Appl, 2005, 403:45-52
  • 5Hasanov Vejdi I. Positive definite solutions of the matrix equations X ± A*X-qA = Q. Linear Algebra Appl, 2005, 404:166-182
  • 6Ran 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
  • 7E1-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
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  • 9Mohamed 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.
  • 10Salah 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.

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数学的实践与认识
2015年 第8期

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