Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots
We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/410410 |
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| author | Fiza Zafar Nawab Hussain Zirwah Fatimah Athar Kharal |
| author_facet | Fiza Zafar Nawab Hussain Zirwah Fatimah Athar Kharal |
| author_sort | Fiza Zafar |
| collection | DOAJ |
| description | We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton’s method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method. |
| format | Article |
| id | doaj-art-80e35b30d08a4f1d8cf379de5d7c6cc9 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-80e35b30d08a4f1d8cf379de5d7c6cc92025-02-03T01:06:51ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/410410410410Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing RootsFiza Zafar0Nawab Hussain1Zirwah Fatimah2Athar Kharal3Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, PakistanDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaCentre for Advanced Studies in Pure and Applied Mathematics (CASPAM), Bahauddin Zakariya University, Multan 60800, PakistanNational University of Sciences and Technology (NUST), Islamabad 44000, PakistanWe have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton’s method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.http://dx.doi.org/10.1155/2014/410410 |
| spellingShingle | Fiza Zafar Nawab Hussain Zirwah Fatimah Athar Kharal Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots The Scientific World Journal |
| title | Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots |
| title_full | Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots |
| title_fullStr | Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots |
| title_full_unstemmed | Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots |
| title_short | Optimal Sixteenth Order Convergent Method Based on Quasi-Hermite Interpolation for Computing Roots |
| title_sort | optimal sixteenth order convergent method based on quasi hermite interpolation for computing roots |
| url | http://dx.doi.org/10.1155/2014/410410 |
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