On Approximate GCDs of Univariate Polynomials
نویسندگان
چکیده
منابع مشابه
Certiied Approximate Univariate Gcds
We study the approximate GCD of two univariate polynomials given with limited accuracy or, equivalently, the exact GCD of the perturbed polynomials within some prescribed tolerance. A perturbed polynomial is regarded as a family of polynomials in a clas-siication space, which leads to an accurate analysis of the computation. Considering only the Sylvester matrix singular values, as is frequentl...
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The problem of computing approximate GCDs of several polynomials with real or complex coefficients can be formulated as computing the minimal perturbation such that the perturbed polynomials have an exact GCD of given degree. We present algorithms based on SOS (Sum of Squares) relaxations for solving the involved polynomial or rational function optimization problems with or without constraints.
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We propose a fast algorithm for computing approximate GCD of univariate polynomials with coefficients that are given only to a finite accuracy. The algorithm is based on a stabilized version of the generalized Schur algorithm for Sylvester matrix and its embedding. All computations can be done in O(n2) operations, where n is the sum of the degrees of polynomials. The stability of the algorithm ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1998
ISSN: 0747-7171
DOI: 10.1006/jsco.1998.0232