HOlder条件下求解重根的Traub算法的收敛半径

Convergence Radius of Traub's Method for Multiple Roots under HOlder Continuous Condition

2010年任宏民和Argyros^([1])对求解重根的牛顿法的收敛半径进行了分析,首次给出了重根迭代局部收敛性的分析方法.2011年毕惟红等人基于该思路计算了Halley算法的收敛半径,2018年JoséL等人给出了Osada算法的收敛半径.而对于非线性方程重根迭代算法中,Traub算法至今无人研究,本文将基于任红民和Argyros给出的基本思路计算Traub算法的收敛半径,并通过具体实例进行分析.

In 2010,Ren Hongmin and Argeryros[1]analyzed the convergence radius of Newton’s method for solving multiple roots,and gave the local convergence analysis method for iteration of multiple roots for the first time.In 2011,Bi Weihong and others calculated the convergence radius of Halley algorithm based on this idea.In 2018,Jos L and others gave the convergence radius of Osada algorithm.Traub algorithm has not been studied in the iteration algorithm of multiple roots for non-linear equations.This paper will calculate the convergence radius of Traub algorithm based on Ren Hongmin and Arguyros’basic ideas,and analyze it through specific examples.