GPGCD, an Iterative Method for Calculating Approximate GCD of Univariate Polynomials, with the Complex Coefficients - Mathematics > Commutative AlgebraReportar como inadecuado




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Abstract: We present an extension of our GPGCD method, an iterative method forcalculating approximate greatest common divisor GCD of univariatepolynomials, to polynomials with the complex coefficients. For a given pair ofpolynomials and a degree, our algorithm finds a pair of polynomials which has aGCD of the given degree and whose coefficients are perturbed from those in theoriginal inputs, making the perturbations as small as possible, along with theGCD. In our GPGCD method, the problem of approximate GCD is transfered to aconstrained minimization problem, then solved with a so-called modified Newtonmethod, which is a generalization of the gradient-projection method, bysearching the solution iteratively. While our original method is designed forpolynomials with the real coefficients, we extend it to accept polynomials withthe complex coefficients in this paper.



Autor: Akira Terui

Fuente: https://arxiv.org/







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