Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations
In nonlinear problems where function’s derivatives are difficult or expensive to compute, derivative-free iterative methods are good options to find the numerical solution. One of the important parts in the development of such methods is to study their convergence properties. In this paper, we revie...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Ada Academica
2023-09-01
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| Series: | European Journal of Mathematical Analysis |
| Online Access: | https://adac.ee/index.php/ma/article/view/170 |
| _version_ | 1797388640578437120 |
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| author | Sunil Kumar Janak Raj Sharma Ioannis K. Argyros Samundra Regmi |
| author_facet | Sunil Kumar Janak Raj Sharma Ioannis K. Argyros Samundra Regmi |
| author_sort | Sunil Kumar |
| collection | DOAJ |
| description | In nonlinear problems where function’s derivatives are difficult or expensive to compute, derivative-free iterative methods are good options to find the numerical solution. One of the important parts in the development of such methods is to study their convergence properties. In this paper, we review the concepts of local and semi-local convergence for a derivative-free method for nonlinear equations. In the earlier study of the considered method, the convergence analysis was carried out assuming the existence of higher order derivatives while no derivative is used in the method. Such assumptions certainly restrict its applicability. The present study further provides the estimate of convergence radius and bounds on the error for the given method. Thus, the applicability of the method clearly seems to be extended over the wider class of problems. We also review some of the recent developments in this area. The results presented in this paper can be useful for practitioners and researchers in developing and analyzing derivative-free numerical algorithms. |
| first_indexed | 2024-03-08T22:43:43Z |
| format | Article |
| id | doaj.art-d8b8472416d24f878b02b460e06061de |
| institution | Directory Open Access Journal |
| issn | 2733-3957 |
| language | English |
| last_indexed | 2024-03-08T22:43:43Z |
| publishDate | 2023-09-01 |
| publisher | Ada Academica |
| record_format | Article |
| series | European Journal of Mathematical Analysis |
| spelling | doaj.art-d8b8472416d24f878b02b460e06061de2023-12-17T08:35:04ZengAda AcademicaEuropean Journal of Mathematical Analysis2733-39572023-09-013242410.28924/ada/ma.3.24170Seventh Order Derivative-Free Methods for Non-differentiable Operator EquationsSunil Kumar0Janak Raj Sharma1Ioannis K. Argyros2Samundra Regmi3Department of Mathematics, University Centre for Research and Development, Chandigarh University, Mohali-140413, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering & Technology, Longowal, Punjab 148106, IndiaDepartment of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USADepartment of Mathematics, University of Houston, Houston, TX, 77024, USAIn nonlinear problems where function’s derivatives are difficult or expensive to compute, derivative-free iterative methods are good options to find the numerical solution. One of the important parts in the development of such methods is to study their convergence properties. In this paper, we review the concepts of local and semi-local convergence for a derivative-free method for nonlinear equations. In the earlier study of the considered method, the convergence analysis was carried out assuming the existence of higher order derivatives while no derivative is used in the method. Such assumptions certainly restrict its applicability. The present study further provides the estimate of convergence radius and bounds on the error for the given method. Thus, the applicability of the method clearly seems to be extended over the wider class of problems. We also review some of the recent developments in this area. The results presented in this paper can be useful for practitioners and researchers in developing and analyzing derivative-free numerical algorithms.https://adac.ee/index.php/ma/article/view/170 |
| spellingShingle | Sunil Kumar Janak Raj Sharma Ioannis K. Argyros Samundra Regmi Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations European Journal of Mathematical Analysis |
| title | Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations |
| title_full | Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations |
| title_fullStr | Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations |
| title_full_unstemmed | Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations |
| title_short | Seventh Order Derivative-Free Methods for Non-differentiable Operator Equations |
| title_sort | seventh order derivative free methods for non differentiable operator equations |
| url | https://adac.ee/index.php/ma/article/view/170 |
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