An algorithm for computing certified approximate GCD of \(n\) univariate polynomials

DOI10.1016/S0022-4049(99)00014-6zbMath0964.12007OpenAlexW2109445883WikidataQ126351598 ScholiaQ126351598MaRDI QIDQ1295792

David Rupprecht

Publication date: 26 June 2000

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-4049(99)00014-6

zbMATH Keywords

Sylvester matricesSingular Value DecompositionApproximate GCD

Mathematics Subject Classification ID

Related Items (23)

Numerical and Symbolical Methods for the GCD of Several Polynomials ⋮ Structured matrix methods computing the greatest common divisor of polynomials ⋮ The calculation of the degree of an approximate greatest common divisor of two polynomials ⋮ Approximate GCD of several univariate polynomials with small degree perturbations ⋮ The computation of multiple roots of a polynomial ⋮ Approximate polynomial GCD over integers ⋮ Overdetermined Weierstrass iteration and the nearest consistent system ⋮ Computation of the topology of real algebraic space curves ⋮ Recursive polynomial remainder sequence and its subresultants ⋮ Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation ⋮ Computing multiple roots of inexact polynomials ⋮ Regularization and Matrix Computation in Numerical Polynomial Algebra ⋮ The ERES method for computing the approximate GCD of several polynomials ⋮ Approximate polynomial GCD by approximate syzygies ⋮ GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials ⋮ Approximate polynomial GCD: small degree and small height perturbations ⋮ Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials ⋮ Blind image deconvolution through Bezoutians ⋮ A computational study of ruled surfaces ⋮ Nearest common root of a set of polynomials: a structured singular value approach ⋮ Computing greatest common divisors and squarefree decompositions through matrix methods: the parametric and approximate cases ⋮ An ODE-Based Method for Computing the Distance of Coprime Polynomials to Common Divisibility ⋮ Variable projection methods for approximate (greatest) common divisor computations

Cites Work

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• Products of polynomials in many variables
• Quasi-gcd computations
• Certified approximate univariate GCDs
• Detection and validation of clusters of polynomial zeros

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