Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation
This article explores the application of exact line search and successive over-relaxation techniques to enhance the convergence of Newton method in solving the Yang-Baxter matrix equation for nontrivial numerical solutions. Moreover, the normwise, mixed, and componentwise condition numbers are deriv...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844025008059 |
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| author | Chacha Stephen Chacha |
| author_facet | Chacha Stephen Chacha |
| author_sort | Chacha Stephen Chacha |
| collection | DOAJ |
| description | This article explores the application of exact line search and successive over-relaxation techniques to enhance the convergence of Newton method in solving the Yang-Baxter matrix equation for nontrivial numerical solutions. Moreover, the normwise, mixed, and componentwise condition numbers are derived to assess the sensitivity of solutions. Numerical experiments demonstrate that the exact line search method significantly improves convergence speed, particularly for larger matrices, by reducing both the number of iterations and residuals more effectively than the successive over-relaxation technique. Furthermore, the mixed and componentwise condition numbers consistently yield values close to one, indicating that the Yang-Baxter equation is well-conditioned. In contrast, the relatively high normwise condition numbers suggest an increased sensitivity to perturbations. |
| format | Article |
| id | doaj-art-53088c5c4cbb4f82a9dd06fff075f866 |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-53088c5c4cbb4f82a9dd06fff075f8662025-02-05T04:32:22ZengElsevierHeliyon2405-84402025-02-01113e42425Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equationChacha Stephen Chacha0Department of Mathematics, Physics and Informatics, Mkwawa University College of Education, P.O. Box 2513, Iringa, TanzaniaThis article explores the application of exact line search and successive over-relaxation techniques to enhance the convergence of Newton method in solving the Yang-Baxter matrix equation for nontrivial numerical solutions. Moreover, the normwise, mixed, and componentwise condition numbers are derived to assess the sensitivity of solutions. Numerical experiments demonstrate that the exact line search method significantly improves convergence speed, particularly for larger matrices, by reducing both the number of iterations and residuals more effectively than the successive over-relaxation technique. Furthermore, the mixed and componentwise condition numbers consistently yield values close to one, indicating that the Yang-Baxter equation is well-conditioned. In contrast, the relatively high normwise condition numbers suggest an increased sensitivity to perturbations.http://www.sciencedirect.com/science/article/pii/S2405844025008059Matrix equationNormwise, mixed, and componentwise condition numbersExact line searchSuccessive over-relaxation |
| spellingShingle | Chacha Stephen Chacha Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation Heliyon Matrix equation Normwise, mixed, and componentwise condition numbers Exact line search Successive over-relaxation |
| title | Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation |
| title_full | Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation |
| title_fullStr | Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation |
| title_full_unstemmed | Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation |
| title_short | Accelerating the convergence of Newton's method for the Yang-Baxter like matrix equation |
| title_sort | accelerating the convergence of newton s method for the yang baxter like matrix equation |
| topic | Matrix equation Normwise, mixed, and componentwise condition numbers Exact line search Successive over-relaxation |
| url | http://www.sciencedirect.com/science/article/pii/S2405844025008059 |
| work_keys_str_mv | AT chachastephenchacha acceleratingtheconvergenceofnewtonsmethodfortheyangbaxterlikematrixequation |