On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions

被引：19
|
作者：
Hernandez-Veron, M. A. [1 ]
Martinez, Eulalia [2 ]
机构：
[1] Univ La Rioja, Dept Math & Computat, Logrono 26004, Spain
[2] Univ Politecn Valencia, Inst Matemat Pura & Aplicada, Valencia 4602, Spain
来源：
NUMERICAL ALGORITHMS | 2015年 / 70卷 / 02期
关键词：
Nonlinear equations; Order of convergence; Iterative methods; Semilocal convergence; Hammerstein equation;
D O I：
10.1007/s11075-014-9952-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper the semilocal convergence for an alternative to the three steps Newton's method with frozen derivative is presented. We analyze the generalization of convergence conditions given by w-conditioned non-decreasing functions instead of the first derivative Lipschitz or Holder continuous given by other authors. A nonlinear integral equation of mixed Hammerstein type is considered for illustrating the new theoretical results obtained in this paper, where previous results can not be satisfied.
引用
收藏
页码：377 / 392
页数：16
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