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

Autor: Mohamed A. Ramadan, Naglaa M. El–Shazly
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Zdroj: Journal of the Egyptian Mathematical Society, Vol 28, Iss 1, Pp 1-13 (2020)
Druh dokumentu: article
ISSN: 2090-9128
DOI: 10.1186/s42787-019-0052-7
Popis: 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.
Databáze: Directory of Open Access Journals
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