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On positive definite solution of a nonlinear matrix equation |
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| Authors: | Zhen‐yun Peng Salah M El‐Sayed |
| Institution: | 1. Department of Mathematics, Hunan University of Science and Technology, Xiangtan 411201, People's Republic of ChinaDepartment of Mathematics, Hunan University of Science and Technology, Xiangtan 411201, People's Republic of China===;2. Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt |
| Abstract: | In this paper, some necessary and sufficient conditions for the existence of the positive definite solutions for the matrix equation X + A*X?αA = Q with α ∈ (0, ∞) are given. Iterative methods to obtain the positive definite solutions are established and the rates of convergence of the considered methods are obtained. Copyright © 2006 John Wiley & Sons, Ltd. |
| Keywords: | nonlinear matrix equation positive definite matrix iterative methods the maximal positive definite solution the minimal positive definite solution |