Extended semilocal convergence for the Newton- Kurchatov method
We provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general. A convergence of this method is presented under classical Lipschitz conditions. The novelty of our paper...
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Ivan Franko National University of Lviv
2020-03-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/3 |
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| author | H.P. Yarmola I. K. Argyros S.M. Shakhno |
| author_facet | H.P. Yarmola I. K. Argyros S.M. Shakhno |
| author_sort | H.P. Yarmola |
| collection | DOAJ |
| description | We provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general. A convergence of this method is presented under classical Lipschitz conditions.
The novelty of our paper lies in the fact that we obtain weaker sufficient semilocal convergence criteria and tighter error estimates than in earlier works. We find a more precise location than before where the iterates lie resulting to at least as small Lipschitz constants. Moreover, no additional computations are needed than before. Finally, we give results of numerical experiments. |
| format | Article |
| id | doaj-art-0da1c75df82c46e2beecd0e0d2be78c2 |
| institution | DOAJ |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2020-03-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-0da1c75df82c46e2beecd0e0d2be78c22025-08-20T02:41:33ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202020-03-01531859110.30970/ms.53.1.85-913Extended semilocal convergence for the Newton- Kurchatov methodH.P. Yarmola0I. K. Argyros1S.M. Shakhno2Department of Computational Mathematics, Ivan Franko National University of Lviv, Lviv, UkraineDepartment of Mathematics, Cameron University, Lawton, USADepartment of Theory of Optimal Processes, Ivan Franko National University of Lviv, Lviv, UkraineWe provide a semilocal analysis of the Newton-Kurchatov method for solving nonlinear equations involving a splitting of an operator. Iterative methods have a limited restricted region in general. A convergence of this method is presented under classical Lipschitz conditions. The novelty of our paper lies in the fact that we obtain weaker sufficient semilocal convergence criteria and tighter error estimates than in earlier works. We find a more precise location than before where the iterates lie resulting to at least as small Lipschitz constants. Moreover, no additional computations are needed than before. Finally, we give results of numerical experiments.http://matstud.org.ua/ojs/index.php/matstud/article/view/3nonlinear equation; newton-kurchatov method; semilocal convergence; decomposition of operator |
| spellingShingle | H.P. Yarmola I. K. Argyros S.M. Shakhno Extended semilocal convergence for the Newton- Kurchatov method Математичні Студії nonlinear equation; newton-kurchatov method; semilocal convergence; decomposition of operator |
| title | Extended semilocal convergence for the Newton- Kurchatov method |
| title_full | Extended semilocal convergence for the Newton- Kurchatov method |
| title_fullStr | Extended semilocal convergence for the Newton- Kurchatov method |
| title_full_unstemmed | Extended semilocal convergence for the Newton- Kurchatov method |
| title_short | Extended semilocal convergence for the Newton- Kurchatov method |
| title_sort | extended semilocal convergence for the newton kurchatov method |
| topic | nonlinear equation; newton-kurchatov method; semilocal convergence; decomposition of operator |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/3 |
| work_keys_str_mv | AT hpyarmola extendedsemilocalconvergenceforthenewtonkurchatovmethod AT ikargyros extendedsemilocalconvergenceforthenewtonkurchatovmethod AT smshakhno extendedsemilocalconvergenceforthenewtonkurchatovmethod |