A new family of fourth-order methods for multiple roots of nonlinear equations

被引：39
作者：
Liu, Baoqing [1 ]
Zhou, Xiaojian [1 ,2 ]
机构：
[1] Nanjing Normal Univ, Sch Math Sci, Inst Math, Jiangsu Key Lab NSLSCS, Nanjing 210023, Jiangsu, Peoples R China
[2] Nantong Univ, Sch Sci, Nantong 226008, Peoples R China
来源：
NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2013年 / 18卷 / 02期
基金：
中国国家自然科学基金;
关键词：
nonlinear equations; iterative method; multiple roots; the modified Newton's method; optimal order; ORDER;
D O I：
10.15388/NA.18.2.14018
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, some optimal fourth-order iterative methods for multiple roots of nonlinear equations are presented when the multiplicity m of the root is known. Different from these optimal iterative methods known already, this paper presents a new family of iterative methods using the modified Newton's method as its first step. The new family, requiring one evaluation of the function and two evaluations of its first derivative, is of optimal order. Numerical examples are given to suggest that the new family can be competitive with other fourth-order methods and the modified Newton's method for multiple roots.
引用
收藏
页码：143 / 152
页数：10
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