期刊
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
卷 373, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.cam.2019.112380
关键词
Matrix equation; Symmetric positive definite; Fixed-point iteration; Thompson metric; Geometric mean; Perturbation analysis
资金
- Basic Science Research Program through the National Research Foundation of Korea, South Korea - Ministry of Education [NRF-2018R1D1A1B07049948]
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Education [2017R1D1A3B04033516]
- National Research Foundation of Korea (NRF), South Korea Grant - Korean Government (MSIP) [NRF-2017R1A5A1015722]
- National Research Foundation of Korea, South Korea - Ministry of Education [NRF-2019R1I1A1A01062548]
- National Research Foundation of Korea [2017R1D1A3B04033516] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
The nonlinear matrix equation X-p = A + M-T (X#B)M, where p >= 1 is a positive integer, M is an n x n nonsingular matrix, A is a positive semidefinite matrix and B is a positive definite matrix, is considered. We denote by C#D the geometric mean of positive definite matrices C and D. Based on the properties of the Thompson metric, we prove that this nonlinear matrix equation always has a unique positive definite solution and that the fixed-point iteration method can be efficiently employed to compute it. In addition, estimates of the positive definite solution and perturbation analysis are investigated. Numerical experiments are given to confirm the theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved.
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