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: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/3291867 |
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| _version_ | 1850214996080852992 |
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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. |
| format | Article |
| id | doaj-art-7fa6fe9abd184f1486476333b4e8620a |
| institution | OA Journals |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| 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 |