Fast and efficient parallel evaluation of the zeros of a polynomial having only real zeros

Abstract

Given a polynomial p( x) of degree n with integer coefficients between −2 m and 2 m it suffices to use O(log 2 n+log b)) parallel arithmetic steps and n 2 processors in order to compute all the zeros of p( x) with absolute errors at most 2 − h provided that all the zeros are real and b = m + h. The algorithm combines the recent techniques and results of [1–3] in order to improve the previous record processor bound of [1] at least on the factor of n (preserving its upper bound on parallel time).