ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A^＊X^-2 A=I 被引量：1

ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A^＊X^-2 A=I

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摘要 The Hermitian positive definite solutions of the matrix equation X-A^＊X^-2 A=I are studied. A theorem for existence of solutions is given for every complex matrix A. A solution in case A is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given. The Hermitian positive definite solutions of the matrix equation X-A^＊X^-2 A=I are studied. A theorem for existence of solutions is given for every complex matrix A. A solution in case A is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.

作者 Yu-hai Zhang

机构地区 School of Mathematics and System Sciences

出处《Journal of Computational Mathematics》 SCIE CSCD 2005年第4期408-418,共11页 计算数学（英文）

关键词 Matrix equation Positive definite solution Iterative methods Matrix equation, Positive definite solution, Iterative methods

分类号 O15 [理学—基础数学]

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1R. Akerkar, Nonlinear Functional analysis, Narosa Publishing House, London, 1999.
2R. Bhatia, Matrix Analysis, Springer, New York, 1997.
3J.C. Engwerda, On the existence of a positive definite solution of the matrix equation X +A^T X^-1A = I, Linear Algebra Appl, 194 (1993), 91-108.
4J.C. Engwerda, A.C.M. Ran and A.L. Rijkeboer, Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X + A^TX^-1A = Q, Linear Algebra Appl, 186 (1993), 255-275.
5C. Guo and P. Lancaster, Iterative solution of two matrix equations, Math. Comp., 68:228 (1999),1589-1603.
6V.I. Hasanov, Solutions and perturbation theory of nonlinear matrix equations, PhD thesis, Sofia 2003.
7I.G. Ivanov and S.M. E1-Sayed, Properties of positive definite solution of the equation X+A^*X^-2A = I, Linear Algebra Appl., 279 (1998), 303-316.
8I.G. Ivanov, V.I. Hasanov and B.V. Minchev, On matrix equations X ± A^*X^-2A = I, Linear Algebra Appl., 326 (2001), 27-44.
9X.-G. Liu and H. Gao, On the positive definite solutions of the matrix equations X8±A^TX^-tA =In, Linear Algebra Appl., 368 (2003), 83-97.
10I.C.M. Ran and M.C.B. Reurings, On the nonlinear matrix equation X + A^*F(X)A =Q:solution and perturbation theory, Linear Algebra Appl., 346 (2002), 15-26.