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Structured low rank approximation of a Bezout matrix. (English) Zbl 1132.68073

Summary: 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) method for computing approximate GCD and demonstrate the practical performance of our algorithm on a diverse set of univariate polynomials.

MSC:

68W30 Symbolic computation and algebraic computation
65K10 Numerical optimization and variational techniques

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