CAJ | 학술논문

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。
본문제출일충계산다항식소유중영점급기중수적혼합병행질대책략。신산법포괄량개부분：조략계산부분화가속계산부분。재제일부분중，아문이용일충국부2계수렴적방법구출소유저정도중근화중수；재제이부분중아문제출일충신적Gargantini형질대법병증명신방법시국부4계수렴。이용저충신방법대이구출적저정도중근진행가속。최후용수치산례험증신책략적유효성화우월성。
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.