On the perturbation analysis of the maximal solution for the matrix equation X−∑i=1mAi∗X−1Ai+∑j=1nBj∗X−1Bj=I $$ X-\overset{m}{\sum \limits_{i=1}}{A}_i^{\ast}\kern0.1em {X}^{-1}\kern0.1em {A}_i+\sum \limits_{j=1}^n{B}_j^{\ast}\kern0.1em {X}^{-1}\kern0.1em {B}_j=I $$

Journal of the Egyptian Mathematical Society

Naglaa M. El–Shazly¹  Mohamed A. Ramadan¹ 

[1] Department of Mathematics and Computer Science, Faculty of Science, Menoufia University;

关键词: Nonlinear matrix equation;    Maximal positive solution;    Iteration;    Matrix differentiation;    Perturbation bound;   

DOI  :  10.1186/s42787-019-0052-7

来源: DOAJ

【 摘 要 】

Abstract In this paper, we study the perturbation estimate of the maximal solution for the matrix equation X−∑i=1mAi∗X−1Ai+∑j=1nBj∗X−1Bj=I $$ X-\overset{m}{\sum \limits_{i=1}}{A}_i^{\ast}\kern0.1em {X}^{-1}\kern0.1em {A}_i+\sum \limits_{j=1}^n{B}_j^{\ast}\kern0.1em {X}^{-1}\kern0.1em {B}_j=I $$ using the differentiation of matrices. We derive the differential bound for this maximal solution. Moreover, we present a perturbation estimate and an error bound for this maximal solution. Finally, a numerical example is given to clarify the reliability of our obtained results.

【 授权许可】

Unknown