A family of Steffensen type methods with seventh-order convergence

被引：56
|
作者：
Wang, Xiaofeng [1 ,2 ]
Zhang, Tie [1 ]
机构：
[1] Northeastern Univ, Coll Sci, Shenyang 110819, Liaoning, Peoples R China
[2] Bohai Univ, Dept Math, Jinzhou 121013, Liaoning, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2013年 / 62卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Steffensen's method; Newton's method; Derivative free; Seventh-order convergence; Root-finding; NONLINEAR EQUATIONS; SYSTEMS;
D O I：
10.1007/s11075-012-9597-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, based on some known fourth-order Steffensen type methods, we present a family of three-step seventh-order Steffensen type iterative methods for solving nonlinear equations and nonlinear systems. For nonlinear systems, a development of the inverse first-order divided difference operator for multivariable function is applied to prove the order of convergence of the new methods. Numerical experiments with comparison to some existing methods are provided to support the underlying theory.
引用
收藏
页码：429 / 444
页数：16
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