On the Hermitian positive defnite solution of the nonlinear matrix equation X + A*X
−1
A + B*X
−1
B = I |
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| Authors: | Jian-hui Long Xi-yan Hu Lei Zhang |
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| Institution: | (1) College of Mathematics, Changsha, 410082, China;(2) Department of Mathematics and Physics, Fujian University of Technology, Fuzhou, 350014, China;(3) College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China |
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| Abstract: | In this paper, we study the matrix equation X + A*X
−1
A + B*X
−1
B = I, where A, B are square matrices, and obtain some conditions for the existence of the positive definite solution of this equation. Two
iterative algorithms to find the positive definite solution are given. Some numerical results are reported to illustrate the
effectiveness of the algorithms.
This research supported by the National Natural Science Foundation of China 10571047 and Doctorate Foundation of the Ministry
of Education of China 20060532014. |
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| Keywords: | nonlinear matrix equation positive definite solution iterative method |
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