Abstract

A practical version of a parallel algorithm that approximates the roots of a polynomial whose roots are all real is developed using the ideas of an existing NC algorithm. An new elementary proof of correctness is provided and the complexity of the algorithm is analyzed. A particular implementation of the algorithm that performs well in practice is described and its run-time behaviour is compared with the analytical predictions. 1 Introduction In this paper we describe and analyze the behaviour of an implementation of a parallel algorithm that approximates the roots of a polynomial which has only real roots. The polynomial root approximation problem we consider can be defined as follows. Given a positive integer ¯, and a polynomial p 0 (x) of degree n, whose coefficients are m-bit integers and whose roots x 1 ; x 2 ; . . . ; x n are all real, we wish to compute ¯-approximations ~ x 1 ; ~ x 2 ; . . . ; ~ x n respectively to these roots, where the ¯-approximation ~ x i to the root x i i...

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