A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones
In order to compare different solvers for systems of nonlinear equations, some novel goodness and qualification criteria are defined in this paper. These use all parameters of a nonlinear solver such as convergence order, number of function evaluations, number of iterations, CPU time, etc. To achiev...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/4327913 |
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| author | R. H. AL-Obaidi M. T. Darvishi |
| author_facet | R. H. AL-Obaidi M. T. Darvishi |
| author_sort | R. H. AL-Obaidi |
| collection | DOAJ |
| description | In order to compare different solvers for systems of nonlinear equations, some novel goodness and qualification criteria are defined in this paper. These use all parameters of a nonlinear solver such as convergence order, number of function evaluations, number of iterations, CPU time, etc. To achieve the criteria, different algorithms to solve nonlinear systems are categorised to three kinds. For any category, two criteria are defined to compare different algorithms in that category. As numerical results show, these new criteria can use to compare different algorithms which solve systems of nonlinear equations. Further, we present some corrected formulas for some classical efficiency indices and change them to be more applicable. Also, some suggestions are presented about the future works. |
| format | Article |
| id | doaj-art-c76cae3862f342e3b840b3c8ad7b9191 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c76cae3862f342e3b840b3c8ad7b91912025-02-03T01:23:34ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/4327913A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New OnesR. H. AL-Obaidi0M. T. Darvishi1Department of MathematicsDepartment of MathematicsIn order to compare different solvers for systems of nonlinear equations, some novel goodness and qualification criteria are defined in this paper. These use all parameters of a nonlinear solver such as convergence order, number of function evaluations, number of iterations, CPU time, etc. To achieve the criteria, different algorithms to solve nonlinear systems are categorised to three kinds. For any category, two criteria are defined to compare different algorithms in that category. As numerical results show, these new criteria can use to compare different algorithms which solve systems of nonlinear equations. Further, we present some corrected formulas for some classical efficiency indices and change them to be more applicable. Also, some suggestions are presented about the future works.http://dx.doi.org/10.1155/2022/4327913 |
| spellingShingle | R. H. AL-Obaidi M. T. Darvishi A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones Journal of Mathematics |
| title | A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones |
| title_full | A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones |
| title_fullStr | A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones |
| title_full_unstemmed | A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones |
| title_short | A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones |
| title_sort | comparative study on qualification criteria of nonlinear solvers with introducing some new ones |
| url | http://dx.doi.org/10.1155/2022/4327913 |
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