Dynamical Techniques for Analyzing Iterative Schemes with Memory
We construct a new biparametric three-point method with memory to highly improve the computational efficiency of its original partner, without adding functional evaluations. In this way, through different estimations of self-accelerating parameters, we have modified an existing seventh-order method....
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/1232341 |
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| author | Neha Choubey A. Cordero J. P. Jaiswal J. R. Torregrosa |
| author_facet | Neha Choubey A. Cordero J. P. Jaiswal J. R. Torregrosa |
| author_sort | Neha Choubey |
| collection | DOAJ |
| description | We construct a new biparametric three-point method with memory to highly improve the computational efficiency of its original partner, without adding functional evaluations. In this way, through different estimations of self-accelerating parameters, we have modified an existing seventh-order method. The parameters have been defined by Hermite interpolating polynomial that allows the accelerating effect. In particular, the R-order of the proposed iterative method with memory is increased from seven to ten. A real multidimensional analysis of the stability of this method with memory is made, in order to study its dependence on the initial estimations. Taking into account that usually iterative methods with memory are more stable than their derivative-free partners and the obtained results in this study, the behavior of this scheme shows to be excellent, but for a small domain. Numerical examples and comparison are also provided, confirming the theoretical results. |
| format | Article |
| id | doaj-art-e2d6c14e55f34da991bcb635169f1c2f |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-e2d6c14e55f34da991bcb635169f1c2f2025-02-03T01:21:50ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/12323411232341Dynamical Techniques for Analyzing Iterative Schemes with MemoryNeha Choubey0A. Cordero1J. P. Jaiswal2J. R. Torregrosa3Department of Mathematics, Oriental Institute of Science and Technology, Bhopal 462021, IndiaInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Cno. de Vera s/n, 46022 València, SpainDepartment of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462051, IndiaInstituto de Matemática Multidisciplinar, Universitat Politècnica de València, Cno. de Vera s/n, 46022 València, SpainWe construct a new biparametric three-point method with memory to highly improve the computational efficiency of its original partner, without adding functional evaluations. In this way, through different estimations of self-accelerating parameters, we have modified an existing seventh-order method. The parameters have been defined by Hermite interpolating polynomial that allows the accelerating effect. In particular, the R-order of the proposed iterative method with memory is increased from seven to ten. A real multidimensional analysis of the stability of this method with memory is made, in order to study its dependence on the initial estimations. Taking into account that usually iterative methods with memory are more stable than their derivative-free partners and the obtained results in this study, the behavior of this scheme shows to be excellent, but for a small domain. Numerical examples and comparison are also provided, confirming the theoretical results.http://dx.doi.org/10.1155/2018/1232341 |
| spellingShingle | Neha Choubey A. Cordero J. P. Jaiswal J. R. Torregrosa Dynamical Techniques for Analyzing Iterative Schemes with Memory Complexity |
| title | Dynamical Techniques for Analyzing Iterative Schemes with Memory |
| title_full | Dynamical Techniques for Analyzing Iterative Schemes with Memory |
| title_fullStr | Dynamical Techniques for Analyzing Iterative Schemes with Memory |
| title_full_unstemmed | Dynamical Techniques for Analyzing Iterative Schemes with Memory |
| title_short | Dynamical Techniques for Analyzing Iterative Schemes with Memory |
| title_sort | dynamical techniques for analyzing iterative schemes with memory |
| url | http://dx.doi.org/10.1155/2018/1232341 |
| work_keys_str_mv | AT nehachoubey dynamicaltechniquesforanalyzingiterativeschemeswithmemory AT acordero dynamicaltechniquesforanalyzingiterativeschemeswithmemory AT jpjaiswal dynamicaltechniquesforanalyzingiterativeschemeswithmemory AT jrtorregrosa dynamicaltechniquesforanalyzingiterativeschemeswithmemory |