On the nonlinear matrix equation Xp = A + MT(X#B)M

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:373

Article; Proceedings Paper

Lee, Hosoo¹  Kim, Hyun-Min^2,3  Meng, Jie³ 

[1] Jeju Natl Univ, Elementary Educ Res Inst, Jeju 63294, South Korea

[2] Pusan Natl Univ, Dept Math, Busan 46241, South Korea

[3] Pusan Natl Univ, Finance Fishery Mfg Ind Math Ctr Big Data, Busan 46241, South Korea

关键词: Matrix equation;    Symmetric positive definite;    Fixed-point iteration;    Thompson metric;    Geometric mean;    Perturbation analysis;   

DOI  :  10.1016/j.cam.2019.112380

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

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