摘要
给出牛顿迭代方法的两个新格式,S im pson牛顿方法和几何平均牛顿方法,证明了它们至少三次收敛到单根,线性收敛到重根.文末给出数值试验,且与其它已知牛顿法做了比较.结果表明收敛性方法具有较好的优越性,它们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.
Two new schemes of Newton＇s method, which are Simpson Newton＇s method and gemetric mean Newtonrs method, are developed and their convergence properties are proved. They are at least third order conw.rgenee near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton＇s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.
出处
《数学的实践与认识》
CSCD
北大核心
2007年第1期72-76,共5页
Mathematics in Practice and Theory
基金
国家自然科学基金(10371111)
郑州轻工业学院校内基金(2004xjj013)
关键词
牛顿迭代法
收敛阶
数值试验
Newton＇s iteration method
convergence order
numerical test
