New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations
A new family of eighth-order derivative-free methods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the opt...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/493456 |
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| _version_ | 1849435207350878208 |
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| author | Rajinder Thukral |
| author_facet | Rajinder Thukral |
| author_sort | Rajinder Thukral |
| collection | DOAJ |
| description | A new family of eighth-order derivative-free methods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured that the multipoint iteration methods, without memory based on n evaluations could achieve optimal convergence order of . Thus, we present new derivative-free methods which agree with Kung and Traub conjecture for . Numerical comparisons are made to demonstrate the performance of the methods presented. |
| format | Article |
| id | doaj-art-df8463c8673c448caab71004d764ac2f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-df8463c8673c448caab71004d764ac2f2025-08-20T03:26:22ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/493456493456New Eighth-Order Derivative-Free Methods for Solving Nonlinear EquationsRajinder Thukral0Padé Research Centre, 39 Deanswood Hill, Leeds, West Yorkshire LS17 5JS, UKA new family of eighth-order derivative-free methods for solving nonlinear equations is presented. It is proved that these methods have the convergence order of eight. These new methods are derivative-free and only use four evaluations of the function per iteration. In fact, we have obtained the optimal order of convergence which supports the Kung and Traub conjecture. Kung and Traub conjectured that the multipoint iteration methods, without memory based on n evaluations could achieve optimal convergence order of . Thus, we present new derivative-free methods which agree with Kung and Traub conjecture for . Numerical comparisons are made to demonstrate the performance of the methods presented.http://dx.doi.org/10.1155/2012/493456 |
| spellingShingle | Rajinder Thukral New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations International Journal of Mathematics and Mathematical Sciences |
| title | New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations |
| title_full | New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations |
| title_fullStr | New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations |
| title_full_unstemmed | New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations |
| title_short | New Eighth-Order Derivative-Free Methods for Solving Nonlinear Equations |
| title_sort | new eighth order derivative free methods for solving nonlinear equations |
| url | http://dx.doi.org/10.1155/2012/493456 |
| work_keys_str_mv | AT rajinderthukral neweighthorderderivativefreemethodsforsolvingnonlinearequations |