Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative
The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and conver...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/682167 |
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| _version_ | 1832565456221765632 |
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| author | Yonghui Ling Xiubin Xu Shaohua Yu |
| author_facet | Yonghui Ling Xiubin Xu Shaohua Yu |
| author_sort | Yonghui Ling |
| collection | DOAJ |
| description | The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established. |
| format | Article |
| id | doaj-art-86fd1b047cba4ad89bcf9fa050e98d8d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-86fd1b047cba4ad89bcf9fa050e98d8d2025-02-03T01:07:32ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/682167682167Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second DerivativeYonghui Ling0Xiubin Xu1Shaohua Yu2Department of Mathematics, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaDepartment of Mathematics, Zhejiang Normal University, Jinhua 321004, ChinaThe present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.http://dx.doi.org/10.1155/2013/682167 |
| spellingShingle | Yonghui Ling Xiubin Xu Shaohua Yu Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative Abstract and Applied Analysis |
| title | Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative |
| title_full | Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative |
| title_fullStr | Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative |
| title_full_unstemmed | Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative |
| title_short | Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative |
| title_sort | convergence behavior for newton steffensen s method under condition of second derivative |
| url | http://dx.doi.org/10.1155/2013/682167 |
| work_keys_str_mv | AT yonghuiling convergencebehaviorfornewtonsteffensensmethodunderconditionofsecondderivative AT xiubinxu convergencebehaviorfornewtonsteffensensmethodunderconditionofsecondderivative AT shaohuayu convergencebehaviorfornewtonsteffensensmethodunderconditionofsecondderivative |