一类四阶牛顿变形方法  

A Family of Fourth-order Convergence Variant Newton′s Methods

作　　者：赵玲玲[1] 王霞[1] 

机构地区：[1]郑州轻工业学院数学与信息科学系,河南郑州450002

出　　处：《数学的实践与认识》2008年第9期102-106,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10701066);郑州轻工业学院教改项目

摘　　要：给出非线性方程求根的一类四阶方法,也是牛顿法的变形方法.证明了方法收敛性,它们至少四次收敛到单根,线性收敛到重根.文末给出数值试验,且与牛顿法及其它牛顿变形法做了比较.结果表明方法具有很好的优越性,它丰富了非线性方程求根的方法,在理论上和应用上都有一定的价值.A family of fourth-order convergence methods of solving roots for nonlinear equation, which are variant Newton＇s method, are given. Their convergence properties are proved. They are at least fourth-order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton-like methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of nonlinear equation and they are important in both theory and application.

关 键 词：牛顿迭代法 四阶收敛 数值试验 

分 类 号：O241[理学—计算数学]