On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I
Ramadan, M., El–Shazly, N. (2020). On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I. EKB Journal Management System, 28(1), 1-13. doi: 10.1186/s42787-019-0052-7
Mohamed A. Ramadan; Naglaa M. El–Shazly. "On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I". EKB Journal Management System, 28, 1, 2020, 1-13. doi: 10.1186/s42787-019-0052-7
Ramadan, M., El–Shazly, N. (2020). 'On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I', EKB Journal Management System, 28(1), pp. 1-13. doi: 10.1186/s42787-019-0052-7
Ramadan, M., El–Shazly, N. On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I. EKB Journal Management System, 2020; 28(1): 1-13. doi: 10.1186/s42787-019-0052-7

On the perturbation analysis of the maximal solution for the matrix equation X− X i¼1 m A i X−1Ai þX n j¼1 B j X−1 Bj ¼ I

Journal of the Egyptian Mathematical Society
Volume 28, Issue 1, June 2020, Pages 1-13    PDF (569.61 K)
DOI: 10.1186/s42787-019-0052-7
Authors
Mohamed A. Ramadan; Naglaa M. El–Shazly
Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt
Abstract
In this paper, we study the perturbation estimate of the maximal solution for
the matrix equation X−
X
i¼1
m
A
i X−1 Ai þXn
j¼1
B
j X−1 Bj ¼ 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.

Keywords
Nonlinear matrix equation; Maximal positive solution; Iteration; Matrix differentiation; Perturbation bound 
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