An algorithm for computing certified approximate GCD of n univariate polynomials

Abstract

We present some results on approximate GCD for univariate polynomials: given n polynomials P 1,…, P n , we would like to find some perturbed polynomials P ̃ 1,…, P ̃ n (w.r.t. a tolerance ε) which have an exact GCD of maximal degree. We use both algebraic tools (generalized Sylvester matrix) and numeric tools (Singular Value Decomposition). We give certification theorems for the degree of an approximate gcd and also algorithms to compute a candidate gcd and the associated perturbed polynomials.