Semilocal Convergence for a Fifth-Order Newton's Method Using Recurrence Relations in Banach Spaces

被引：10
|
作者：
Chen, Liang [1 ,2 ]
Gu, Chuanqing [1 ]
Ma, Yanfang [3 ]
机构：
[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China
[2] Huaibei Normal Univ, Sch Math Sci, Huaibei 235000, Anhui, Peoples R China
[3] Huaibei Normal Univ, Sch Comp Sci & Technol, Huaibei 235000, Anhui, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS | 2011年
关键词：
IMPROVEMENTS;
D O I：
10.1155/2011/786306
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：15
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