On Approximate GCDs of Univariate Polynomials

Abstract

In this paper, we consider computations involving polynomials with inexact coefficients, i.e. with bounded coefficient errors. The presence of input errors changes the nature of questions traditionally asked in computer algebra. For instance, given two polynomials, instead of trying to compute their greatest common divisor, one might now try to compute a pair of polynomials with a non-trivial common divisor close to the input polynomials. We consider the problem of finding approximate common divisors in the context of inexactly specified polynomials. We develop efficient algorithms for the so-called nearest common divisor problem and several of its variants.