A Family of High-Order Parallel Rootfinders for Polynomials

Abstract

In this paper we present a family of parallel iterations of order $m+2$ with parameter $m=0,1,...$ for simultaneous finding all zeros of a polynomial without evaluation of derivatives, which includes the well known Weierstrass-Durand-Dochev-Kerner and Börsch-Supan-Nourein iterations as the special cases for $m$=0 and $m$=1, respectively. Some numerical examples are given.