中心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 Center-Holder Continuous Condition

目前,人们在泰勒展开式的基础上提出了一种新的估算求解重根的迭代算法收敛半径的方法.这种方法已经估算了牛顿法的收敛半径,以及Osada算法和Halley算法求解重根的收敛半径,但是其计算的收敛半径都比较大.将在中心Holder条件下求解重根的Traub算法的收敛半径,并通过具体例子对计算结果进行比较,Traub算法的计算结果明显优于在同等条件下Osada和Halley算法的收敛半径.

at present,people have proposed a new method to estimate the convergence ra-dius of iterative algorithm for solving multiple roots based on Taylor expansion.This method has estimated the convergence radius of Newton method and the convergence radius of Osada algorithm and Halley algorithm for solving multiple roots,but the calculated convergence radius is relatively large.This paper will solve the convergence radius of Traub algorithm with multiple roots under the central Holder condition,and compare the calculation results through specific examples.The calculation result of Traub algorithm is obviously better than that of Osada and Halley algorithm under the same conditions.