Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I

We explore the condition numbers of the nonlinear matrix equation Xp-A⁎eXA=I. Explicit expressions for the normwise, mixed, and componentwise condition numbers are derived. The upper bounds for the mixed and componentwise condition numbers are obtained. The numerical result favors the fact that our...

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Main Authors: Chacha Stephen Chacha, Syed Muhammad Raza Shah Naqvi
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/3291867
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author Chacha Stephen Chacha
Syed Muhammad Raza Shah Naqvi
author_facet Chacha Stephen Chacha
Syed Muhammad Raza Shah Naqvi
author_sort Chacha Stephen Chacha
collection DOAJ
description We explore the condition numbers of the nonlinear matrix equation Xp-A⁎eXA=I. Explicit expressions for the normwise, mixed, and componentwise condition numbers are derived. The upper bounds for the mixed and componentwise condition numbers are obtained. The numerical result favors the fact that our estimations are fairly sharp. Also, the relative upper perturbation bounds give satisfactory results for small perturbations in the input data.
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publishDate 2018-01-01
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spelling doaj-art-7fa6fe9abd184f1486476333b4e8620a2025-08-20T02:08:44ZengWileyJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/32918673291867Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=IChacha Stephen Chacha0Syed Muhammad Raza Shah Naqvi1Department of Mathematics, Pusan National University, Busan 46241, Republic of KoreaDepartment of Mathematics, Pusan National University, Busan 46241, Republic of KoreaWe explore the condition numbers of the nonlinear matrix equation Xp-A⁎eXA=I. Explicit expressions for the normwise, mixed, and componentwise condition numbers are derived. The upper bounds for the mixed and componentwise condition numbers are obtained. The numerical result favors the fact that our estimations are fairly sharp. Also, the relative upper perturbation bounds give satisfactory results for small perturbations in the input data.http://dx.doi.org/10.1155/2018/3291867
spellingShingle Chacha Stephen Chacha
Syed Muhammad Raza Shah Naqvi
Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I
Journal of Function Spaces
title Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I
title_full Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I
title_fullStr Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I
title_full_unstemmed Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I
title_short Condition Numbers of the Nonlinear Matrix Equation Xp-A⁎eXA=I
title_sort condition numbers of the nonlinear matrix equation xp a exa i
url http://dx.doi.org/10.1155/2018/3291867
work_keys_str_mv AT chachastephenchacha conditionnumbersofthenonlinearmatrixequationxpaexai
AT syedmuhammadrazashahnaqvi conditionnumbersofthenonlinearmatrixequationxpaexai