On Newton-Like Methods for Solving Nonlinear Equations  

作　　者：KOU Jisheng LIU Dingyou LI Yitian HE Julin 

机构地区：[1]State Key Laboratory of Water Resources and Hydropower Engineering Sciences, Wuhan University, 8 South Donghu Road Wuhan 430072, China

出　　处：《Geo-Spatial Information Science》2006年第1期76-78,共3页地球空间信息科学学报（英文）

基　　金：FundedbytheNational973ProgramofChina(No.2003CB415200),theNationalNaturalScienceFoundationofChina(No.50379038;No.40474003)andtheNational863ProgramofChina(No.2001AA135081).

摘　　要：In this paper, we present a family of general New to n-like methods with a parametric function for finding a zero of a univariate fu nction, permitting f′(x)=0 in some points. The case of multiple roots is n ot treated. The methods are proved to be quadratically convergent provided the w eak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative meth ods with a variable parameter are developed.In this paper, we present a family of general Newton-like methods with a parametric function for finding a zero of a univariate function, permitting f＇（x）= 0 in some points. The case of multiple roots is not treated. The methods are proved to be quadratically convergent provided the weak condition. Thus the methods remove the severe condition f＇（x）≠0. Based on the general form of the Newton-like methods, a family of new iterative methods with a variable parameter are developed.

关 键 词：Newton method Newton-like method nonlinear equations iteration method 

分 类 号：O241.7[理学—计算数学]