Optimization by parameters in the iterative methods for solving non-linear equations
In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experi...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Mongolian Academy of Sciences
2021-08-01
|
| Series: | Proceedings of the Mongolian Academy of Sciences |
| Subjects: | |
| Online Access: | https://www.mongoliajol.info/index.php/PMAS/article/view/1756 |
| _version_ | 1818231318504275968 |
|---|---|
| author | Tugal Zhanlav Khuder Otgondorj |
| author_facet | Tugal Zhanlav Khuder Otgondorj |
| author_sort | Tugal Zhanlav |
| collection | DOAJ |
| description | In this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency. In particular, we considered a variety of real life problems from different disciplines, e.g., Kepler’s equation of motion, Planck’s radiation law problem, in order to check the applicability and effectiveness of our proposed methods. |
| first_indexed | 2024-12-12T10:48:29Z |
| format | Article |
| id | doaj.art-b4bfd76c7c3c4f40b8a1c3f8fe5b4678 |
| institution | Directory Open Access Journal |
| issn | 2310-4716 2312-2994 |
| language | English |
| last_indexed | 2024-12-12T10:48:29Z |
| publishDate | 2021-08-01 |
| publisher | Mongolian Academy of Sciences |
| record_format | Article |
| series | Proceedings of the Mongolian Academy of Sciences |
| spelling | doaj.art-b4bfd76c7c3c4f40b8a1c3f8fe5b46782022-12-22T00:26:49ZengMongolian Academy of SciencesProceedings of the Mongolian Academy of Sciences2310-47162312-29942021-08-01162210.5564/pmas.v61i02.17561707Optimization by parameters in the iterative methods for solving non-linear equationsTugal Zhanlav0https://orcid.org/0000-0003-0743-5587Khuder Otgondorj1https://orcid.org/0000-0003-1635-7971Simulation and Computing Department, Institute of Mathematics and Digital Technology, Mongolian Academy of Sciences, Ulaanbaatar, MongoliaSchool of Applied Sciences, Mongolian University of Science and Technology, Ulaanbaatar, MongoliaIn this paper, we used the necessary optimality condition for parameters in a two-point iterations for solving nonlinear equations. Optimal values of these parameters fully coincide with those obtained in [6] and allow us to increase the convergence order of these iterative methods. Numerical experiments and the comparison of existing robust methods are included to confirm the theoretical results and high computational efficiency. In particular, we considered a variety of real life problems from different disciplines, e.g., Kepler’s equation of motion, Planck’s radiation law problem, in order to check the applicability and effectiveness of our proposed methods.https://www.mongoliajol.info/index.php/PMAS/article/view/1756iterative methodsoptimal values of parametersiterations with memory |
| spellingShingle | Tugal Zhanlav Khuder Otgondorj Optimization by parameters in the iterative methods for solving non-linear equations Proceedings of the Mongolian Academy of Sciences iterative methods optimal values of parameters iterations with memory |
| title | Optimization by parameters in the iterative methods for solving non-linear equations |
| title_full | Optimization by parameters in the iterative methods for solving non-linear equations |
| title_fullStr | Optimization by parameters in the iterative methods for solving non-linear equations |
| title_full_unstemmed | Optimization by parameters in the iterative methods for solving non-linear equations |
| title_short | Optimization by parameters in the iterative methods for solving non-linear equations |
| title_sort | optimization by parameters in the iterative methods for solving non linear equations |
| topic | iterative methods optimal values of parameters iterations with memory |
| url | https://www.mongoliajol.info/index.php/PMAS/article/view/1756 |
| work_keys_str_mv | AT tugalzhanlav optimizationbyparametersintheiterativemethodsforsolvingnonlinearequations AT khuderotgondorj optimizationbyparametersintheiterativemethodsforsolvingnonlinearequations |