Structured matrix-based methods for polynomial ∈-gcd: analysis and comparisons

Authors:
Dario A. Bini;Paola Boito
Affiliations:
Università di Pisa, Pisa, Italy;Università di Pisa, Pisa, Italy
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

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Abstract

The relationship between univariate polynomial ∈-gcd and factorization of resultant matrices is investigated and several stable and effective algorithms for the computation of an ∈-gcd are proposed. The main result is the design of a practically stable algorithm whose arithmetic cost is quadratic in the degrees of the input polynomials. The algorithm relies on the displacement structure properties of Sylvester and Bézout matrices. Its effectiveness is confirmed by numerical experiments.