Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces
We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are derived, and then an existence-uniquenes...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/786306 |
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| _version_ | 1832562628653744128 |
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| author | Liang Chen Chuanqing Gu Yanfang Ma |
| author_facet | Liang Chen Chuanqing Gu Yanfang Ma |
| author_sort | Liang Chen |
| collection | DOAJ |
| description | We study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations.
The recurrence relations for the method are derived, and then an existence-uniqueness theorem is given to establish the
R-order of the method to be five and a priori error bounds. Finally, a numerical application is presented to demonstrate
our approach. |
| format | Article |
| id | doaj-art-a57e63be714541ab9371a1fadddff702 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a57e63be714541ab9371a1fadddff7022025-02-03T01:22:11ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/786306786306Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach SpacesLiang Chen0Chuanqing Gu1Yanfang Ma2Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaSchool of Computer Science and Technology, Huaibei Normal University, Anhui, Huaibei 235000, ChinaWe study a modified Newton's method with fifth-order convergence for nonlinear equations in Banach spaces. We make an attempt to establish the semilocal convergence of this method by using recurrence relations. The recurrence relations for the method are derived, and then an existence-uniqueness theorem is given to establish the R-order of the method to be five and a priori error bounds. Finally, a numerical application is presented to demonstrate our approach.http://dx.doi.org/10.1155/2011/786306 |
| spellingShingle | Liang Chen Chuanqing Gu Yanfang Ma Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces Journal of Applied Mathematics |
| title | Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces |
| title_full | Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces |
| title_fullStr | Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces |
| title_full_unstemmed | Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces |
| title_short | Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces |
| title_sort | semilocal convergence for a fifth order newton s method using recurrence relations in banach spaces |
| url | http://dx.doi.org/10.1155/2011/786306 |
| work_keys_str_mv | AT liangchen semilocalconvergenceforafifthordernewtonsmethodusingrecurrencerelationsinbanachspaces AT chuanqinggu semilocalconvergenceforafifthordernewtonsmethodusingrecurrencerelationsinbanachspaces AT yanfangma semilocalconvergenceforafifthordernewtonsmethodusingrecurrencerelationsinbanachspaces |