Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation

The ERES Method for Computing the Approximate GCD

The computation of the greatest common divisor (GCD) of a set of polynomials has interested the mathematicians for a long time and has attracted a lot of attention in recent years. A challenging problem that arises from several applications, such as control or image and signal processing, is to develop a numerical GCD method that inherently has the potential to work efficiently with sets of sev...

Numerical and Symbolical Methods Computing the Greatest Common Divisor of Several Polynomials

The computation of the Greatest Common Divisor (GCD) of a set of polynomials is an important issue in computational mathematics and it is linked to Control Theory very strong. In this paper we present different matrix-based methods, which are developed for the efficient computation of the GCD of several polynomials. Some of these methods are naturally developed for dealing with numerical inaccu...

The calculation of the degree of an approximate greatest common divisor of two polynomials

A Lattice Solution to Approximate Common Divisors

The approximate common divisor problem(ACDP) is to find one or more divisors which is the greatest common divisor of the approximate numbers a and b of two given numbers a0 and b0. Howgrave-Graham[7] has considered the special case of b = b0 and gave a continued fraction approach and a lattice approach to find divisors. Furthermore he raised another lattice approach for ACDP based on Coppersmit...

Structured Low Rank Approximation of a Bezout Matrix

The task of determining the approximate greatest common divisor (GCD) of more than two univariate polynomials with inexact coefficients can be formulated as computing for a given Bezout matrix a new Bezout matrix of lower rank whose entries are near the corresponding entries of that input matrix. We present an algorithm based on a version of structured nonlinear total least squares (SNTLS) meth...