Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations
In this work, the following system of nonlinear matrix equations is considered, X1+A∗X1−1A+B∗X2−1B=I and X2+C∗X2−1C+D∗X1−1D=I, where A,B,C, and D are arbitrary n×n matrices and I is the identity matrix of order n. Some conditions for the existence of a positive-definite solution as well as the conve...
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Hindawi Limited
2021
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oai:doaj.org-article:cf77865928df4dbebff9d499c160402d2021-11-08T02:35:43ZLatest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations2314-478510.1155/2021/2667885https://doaj.org/article/cf77865928df4dbebff9d499c160402d2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2667885https://doaj.org/toc/2314-4785In this work, the following system of nonlinear matrix equations is considered, X1+A∗X1−1A+B∗X2−1B=I and X2+C∗X2−1C+D∗X1−1D=I, where A,B,C, and D are arbitrary n×n matrices and I is the identity matrix of order n. Some conditions for the existence of a positive-definite solution as well as the convergence analysis of the newly developed algorithm for finding the maximal positive-definite solution and its convergence rate are discussed. Four examples are also provided herein to support our results.Sourav ShilHemant Kumar NashineHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021) |
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DOAJ |
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DOAJ |
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EN |
| topic |
Mathematics QA1-939 |
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Mathematics QA1-939 Sourav Shil Hemant Kumar Nashine Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations |
| description |
In this work, the following system of nonlinear matrix equations is considered, X1+A∗X1−1A+B∗X2−1B=I and X2+C∗X2−1C+D∗X1−1D=I, where A,B,C, and D are arbitrary n×n matrices and I is the identity matrix of order n. Some conditions for the existence of a positive-definite solution as well as the convergence analysis of the newly developed algorithm for finding the maximal positive-definite solution and its convergence rate are discussed. Four examples are also provided herein to support our results. |
| format |
article |
| author |
Sourav Shil Hemant Kumar Nashine |
| author_facet |
Sourav Shil Hemant Kumar Nashine |
| author_sort |
Sourav Shil |
| title |
Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations |
| title_short |
Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations |
| title_full |
Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations |
| title_fullStr |
Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations |
| title_full_unstemmed |
Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations |
| title_sort |
latest inversion-free iterative scheme for solving a pair of nonlinear matrix equations |
| publisher |
Hindawi Limited |
| publishDate |
2021 |
| url |
https://doaj.org/article/cf77865928df4dbebff9d499c160402d |
| work_keys_str_mv |
AT souravshil latestinversionfreeiterativeschemeforsolvingapairofnonlinearmatrixequations AT hemantkumarnashine latestinversionfreeiterativeschemeforsolvingapairofnonlinearmatrixequations |
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