GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials - 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 multiple polynomial inputs. For a given pair of polynomials anda degree, our algorithm finds a pair of polynomials which has a GCD of thegiven degree and whose coefficients are perturbed from those in the originalinputs, making the perturbations as small as possible, along with the GCD. Inour GPGCD method, the problem of approximate GCD is transferred to aconstrained minimization problem, then solved with the so-called modifiedNewton method, which is a generalization of the gradient-projection method, bysearching the solution iteratively. In this paper, we extend our method toaccept more than two polynomials with the real coefficients as an input.



Autor: Akira Terui

Fuente: https://arxiv.org/



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