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

作　　者：刘兰冬[1] 付云姗[1] 

机构地区：[1]中国矿业大学(北京)理学院数学系,北京100083

出　　处：《工程数学学报》2014年第6期903-914,共12页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11371364);the Fundamental Research Funds for the Central Universities(2009QS09;2010QS03)

摘　　要：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.

关 键 词：多项式零点 同时求根方法 重零点 重根数 收敛阶 

分 类 号：O241.7[理学—计算数学]