q步并行Halley圆盘迭代法的收敛性质

Convergencc Property of the q-Step Parallel Halley Disk Iteration

本文对 q 步并行 Halley 圆盘迭代计算类 PDI(2,q)给出了一个收敛性定理.设 Z_1^(k),…Z_■ ^(k)表示 n 个复圆盘,并设θ^(k)=■ rad Z_i^(k)/■ |Z-midZ_i^(k),其中radZ_i^(k),mid Z_i^(k)分别表示 Z_i^(k)的半径和圆心,而多项式恰有 n 个互异的零点.我们的定理同时表明 PDI(2,q)计算类关于θ^(k)的收敛为3q+1.

In this paper we give a convergence theorem for PDI(2,q),which we call the q-Step Parallel Halley Disk Iteration.Let Z_1^(k),…,Z_n^(k)denote n complex disks.Let θ^(k)=■ rad Z■ / ■ |z-midZ_i^(k)| where radZ_i^(k) and midZ_i^(k) denote the radii and centers of Z_i^(k) respectively and n coincides with the number of the different zeros of the polynomial solved. Our theorem also shows that PDI(2,q)has a convergence rate of 3q+1 order in θ^(k).