ERES

Further numerical aspects of the ERES algorithm for the computation of the greatest common divisor of polynomials and comparison with other existing methodologies. 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.par 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. Analytical examples and the MATLAB implementation (source code) of the ERES algorithm are available from the authors on request.

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References in zbMATH (referenced in 8 articles , 1 standard article )

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  1. Christou, D.; Karcanias, N.; Mitrouli, M.: Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials (2014)
  2. Christou, Dimitrios; Karcanias, Nicos; Mitrouli, Marilena; Triantafyllou, Dimitrios: Numerical and symbolical methods for the GCD of several polynomials (2011)
  3. Karcanias, N.; Fatouros, S.; Mitrouli, M.; Halikias, G. H.: Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation (2006)
  4. Christou, Dimitrios; Mitrouli, Marilena: Estimation of the greatest common divisor of many polynomials using hybrid computations performed by the ERES method (2005)
  5. Triantafyllou, D.; Mitrouli, M.: Two resultant based methods computing the greatest common divisor of two polynomials (2005)
  6. Karcanias, N.; Mitrouli, M.: Normal factorisation of polynomials and computational issues. (2003)
  7. Karcanians, Nicos; Mitrouli, Marilena: Numerical computation of the least common multiple of a set of polynomials (2000)
  8. Mitrouli, M.; Karcanias, N.; Koukouvinos, C.: Further numerical aspects of the ERES algorithm for the computation of the greatest common divisor of polynomials and comparison with other existing methodologies (1996)