On accelerating the convergence of the successive approximations method
In a previous paper of us, we have shown that no q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when \(G^\prime(x^\ast)\) has no eigenvalue equal to 0. However, high convergence orders may be attained if one consid...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2001-02-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://www.ictp.acad.ro/jnaat/journal/article/view/675 |
| _version_ | 1818520905147482112 |
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| author | Emil Cătinaş |
| author_facet | Emil Cătinaş |
| author_sort | Emil Cătinaş |
| collection | DOAJ |
| description |
In a previous paper of us, we have shown that no q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when \(G^\prime(x^\ast)\) has no eigenvalue equal to 0. However, high convergence orders may be attained if one considers perturbed successive approximations.
We characterize the correction terms which must be added at each step in order to obtain convergence with q-order 2 of the resulted iterates.
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| first_indexed | 2024-12-11T01:43:54Z |
| format | Article |
| id | doaj.art-02c84e18638c482da7efbddbb8d51afd |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T01:43:54Z |
| publishDate | 2001-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-02c84e18638c482da7efbddbb8d51afd2022-12-22T01:24:57ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2001-02-01301On accelerating the convergence of the successive approximations methodEmil Cătinaş0Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy In a previous paper of us, we have shown that no q-superlinear convergence to a fixed point \(x^\ast\) of a nonlinear mapping \(G\) may be attained by the successive approximations when \(G^\prime(x^\ast)\) has no eigenvalue equal to 0. However, high convergence orders may be attained if one considers perturbed successive approximations. We characterize the correction terms which must be added at each step in order to obtain convergence with q-order 2 of the resulted iterates. https://www.ictp.acad.ro/jnaat/journal/article/view/675successive approximationsinexact Newton methodsquadratic convergenceacceleration of the convergence of successive approximations |
| spellingShingle | Emil Cătinaş On accelerating the convergence of the successive approximations method Journal of Numerical Analysis and Approximation Theory successive approximations inexact Newton methods quadratic convergence acceleration of the convergence of successive approximations |
| title | On accelerating the convergence of the successive approximations method |
| title_full | On accelerating the convergence of the successive approximations method |
| title_fullStr | On accelerating the convergence of the successive approximations method |
| title_full_unstemmed | On accelerating the convergence of the successive approximations method |
| title_short | On accelerating the convergence of the successive approximations method |
| title_sort | on accelerating the convergence of the successive approximations method |
| topic | successive approximations inexact Newton methods quadratic convergence acceleration of the convergence of successive approximations |
| url | https://www.ictp.acad.ro/jnaat/journal/article/view/675 |
| work_keys_str_mv | AT emilcatinas onacceleratingtheconvergenceofthesuccessiveapproximationsmethod |