GPGCD
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.
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References in zbMATH (referenced in 9 articles , 2 standard articles )
Showing results 1 to 9 of 9.
Sorted by year (- Nagasaka, Kosaku: Toward the best algorithm for approximate GCD of univariate polynomials (2021)
- Bourne, Martin; Winkler, Joab; Su, Yi: The computation of multiple roots of a Bernstein basis polynomial (2020)
- Fazzi, Antonio; Guglielmi, Nicola; Markovsky, Ivan: An ODE-based method for computing the approximate greatest common divisor of polynomials (2019)
- Guglielmi, Nicola; Markovsky, Ivan: An ODE-based method for computing the distance of coprime polynomials to common divisibility (2017)
- Usevich, Konstantin; Markovsky, Ivan: Variable projection methods for approximate (greatest) common divisor computations (2017)
- Terui, Akira: GPGCD: an iterative method for calculating approximate GCD of univariate polynomials (2013)
- Terui, Akira: GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials (2010)
- Terui, Akira: GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials (2010)
- Terui, Akira: GPGCD, an iterative method for calculating approximate GCD of univariate polynomials, with the complex coefficients (2009)