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, Page 1-13 PDF (569.61 K) | ||||
DOI: 10.1186/s42787-019-0052-7 | ||||
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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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