Iterative methods for the extremal positive definite solution of the matrix equation X+A*X-αA=Q

Authors:
Zhen-yun Peng;Salah M. El-Sayed;Xiang-lin Zhang
Affiliations:
Department of Mathematics, Hunan University of Science and Technology, Xiangtan 411201, PR China;Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt;Department of Mathematics, Hunan University of Science and Technology, Xiangtan 411201, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 5
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An improved inversion-free method for solving the matrix equation X+A*X-αA=Q

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Abstract

In this paper, the inversion free variant of the basic fixed point iteration methods for obtaining the maximal positive definite solution of the nonlinear matrix equation X+A^*X^-^@aA=Q with the case 0=1 are proposed. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Numerical examples to illustrate the behavior of the considered algorithms are also given.