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A heuristic verification of the degree of the approximate GCD of two univariate polynomials

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Abstract

We consider the problem of computing verified real interval perturbations of the coefficients of two univariate polynomials such that there exist corresponding perturbed polynomials which have an exact greatest common divisor (GCD) of a given degree k. Based on the certification of the rank deficiency of a submatrix of the Bezout matrix of two univariate polynomials, we propose an algorithm to compute verified real perturbations. Numerical experiments show the performance of our algorithm.

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Authors and Affiliations

  1. Department of Applied Mathematics, School of Science, Changchun University of Science and Technology, Changchun, 130022, China

    Zhe Li

  2. Key Laboratory of Mathematics Mechanization AMSS, Beijing, 100190, China

    Zhe Li & Qi Liu

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  1. Zhe Li
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  2. Qi Liu
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Correspondence to Zhe Li.

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Li, Z., Liu, Q. A heuristic verification of the degree of the approximate GCD of two univariate polynomials. Numer Algor 67, 319–334 (2014). https://doi.org/10.1007/s11075-013-9793-9

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  • DOI: https://doi.org/10.1007/s11075-013-9793-9

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