一种同时求多项式所有零点及其重数的混合并行策略（英文）

A Mixed Parallel Strategy for Determining all Zeros and Multiplicities of a Polynomial

本文提出一种计算多项式所有重零点及其重数的混合并行迭代策略.新算法包括两个部分:粗略计算部分和加速计算部分.在第一部分中,我们利用一种局部2阶收敛的方法求出所有低精度重根和重数;在第二部分中我们提出一种新的Gargantini型迭代法并证明新方法是局部4阶收敛.利用这种新方法对已求出的低精度重根进行加速.最后用数值算例验证新策略的有效性和优越性.

In this paper, a new mixed parallel iterative strategy is designed to determine simul-taneously all multiple zeros and their corresponding multiplicities of a polynomial. The new strategy is consisted of two phases： the rough calculation one and the accelerated calculation one. In phase one, all low accuracy zeros and their corre-sponding multiplicities are computed by a locally second-order convergent method. In phase two, an acceleration of the iterative process is proposed and proved to be a locally fourth-order convergence. By using the new method, all low accuracy zeros are accelerated. Numerical experiments are given to validate the e？ciency and superiority of the new strategy.