GPGCD swMATH ID: 6224 Software Authors: Terui, Akira Description: GPGCD: an approximate polynomial GCD library We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transferred to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. In this paper, we extend our method to accept more than two polynomials with the real coefficients as an input. Homepage: http://code.google.com/p/gpgcd/ Dependencies: Maple Related Software: MultRoot; SLRA; ApaTools; NACLab; IDENT; PSAPSR; Eigtool; GSL; mctoolbox Cited in: 10 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials. Zbl 1290.68139Terui, Akira 2010 GPGCD, an iterative method for calculating approximate GCD of univariate polynomials, with the complex coefficients. Zbl 1186.65063Terui, Akira 2009 all top 5 Cited by 9 Authors 4 Terui, Akira 3 Markovsky, Ivan 2 Guglielmi, Nicola 2 Nagasaka, Kosaku 1 Bourne, Martin 1 Fazzi, Antonio 1 Su, Yi 1 Usevich, Konstantin 1 Winkler, Joab R. all top 5 Cited in 6 Serials 2 Theoretical Computer Science 1 SIAM Journal on Numerical Analysis 1 Journal of Symbolic Computation 1 Numerical Algorithms 1 SIAM Journal on Scientific Computing 1 ACM Communications in Computer Algebra all top 5 Cited in 8 Fields 7 Numerical analysis (65-XX) 5 Field theory and polynomials (12-XX) 5 Computer science (68-XX) 3 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Operations research, mathematical programming (90-XX) 1 Commutative algebra (13-XX) 1 Functions of a complex variable (30-XX) Citations by Year