Further numerical aspects of the ERES algorithm for the computation of the greatest common divisor of polynomials and comparison with other existing methodologies

Abstract

This paper presents the implementation of the ERES numerical method for the computation of the greatest common divisor (GCD) of several polynomials. The ERES algorithm performs row transformations and shifting on a matrix, formed directly from the coefficients of the given polynomials and determines a vector containing the coefficients of the required GCD. A detailed description of the implementation of the algorithm is presented and analytical proofs of its stability are also developed. A comparison of ERES with other iterative matrix-based methods is performed and various numerical results are described.