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384561

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

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Last updated: 05 Jan 2025

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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.

DOI

10.1186/s42787-019-0052-7

Keywords

Nonlinear matrix equation, Maximal positive solution, Iteration, Matrix differentiation, Perturbation bound 

Authors

First Name

Mohamed

Last Name

Ramadan

MiddleName

A.

Affiliation

Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt

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City

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Orcid

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First Name

Naglaa

Last Name

El–Shazly

MiddleName

M.

Affiliation

Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebein El-Koom, Egypt

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Orcid

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Volume

28

Article Issue

1

Related Issue

50535

Issue Date

2020-06-01

Receive Date

2024-10-07

Publish Date

2020-06-01

Page Start

1

Page End

13

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 28_Issue 1_Pages 1-13.pdf

PDF . 583.3kB

Link

https://joems.journals.ekb.eg/article_384561.html

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https://joems.journals.ekb.eg/service?article_code=384561

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384,561

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Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

MainTitle

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

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Type

Article

Created At

21 Dec 2024