Further numerical aspects of the ERES algorithm for the computation of the greatest common divisor of polynomials and comparison with other existing methodologies (Q2785714)

The extended row equivalence and shifting (ERES) method is a new estimating iterative matrix-based method. This paper presents the implementation of the ERES numerical method for the computation of the greatest common divisor of several polynomials. The ERES algorithm performs row transformations and shifting on a matrix formed directly form the coefficients of the given polynomials and determines a vector containing the coefficients of the required greatest common divisor.NEWLINENEWLINENEWLINEA 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. Analytical examples and the MATLAB implementation (source code) of the ERES algorithm are available from the authors on request.