Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation

DOI10.1016/j.camwa.2006.01.010zbMath1134.65334OpenAlexW2074156531MaRDI QIDQ2475938

S. Fatouros, G. H. Halikias, Marilena Mitrouli, Nicos Karcanias

Publication date: 11 March 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.01.010

zbMATH Keywords

numerical examplesresultantsgreatest common divisorpolynomialsfactorisationapproximate computations

Mathematics Subject Classification ID

Related Items (15)

Numerical and Symbolical Methods for the GCD of Several Polynomials ⋮ Computation of the nearest non-prime polynomial matrix: structured low-rank approximation approach ⋮ Approximate zero polynomials of polynomial matrices and linear systems ⋮ An ODE-based method for computing the approximate greatest common divisor of polynomials ⋮ The computation of multiple roots of a polynomial ⋮ Approximate polynomial GCD over integers ⋮ The ERES method for computing the approximate GCD of several polynomials ⋮ Matrix pencil methodologies for computing the greatest common divisor of polynomials: hybrid algorithms and their performance ⋮ Approximate polynomial GCD: small degree and small height perturbations ⋮ Rayleigh quotient methods for estimating common roots of noisy univariate polynomials ⋮ Nearest common root of a set of polynomials: a structured singular value approach ⋮ Generalised resultants, dynamic polynomial combinants and the minimal design problem ⋮ The feedback invariant measures of distance to uncontrollability and unobservability ⋮ Structured low-rank approximation: optimization on matrix manifold approach ⋮ Variable projection methods for approximate (greatest) common divisor computations

Uses Software

• ERES

Cites Work

• Approximate GCD and its application to ill-conditioned algebraic equations
• An algorithm for computing certified approximate GCD of \(n\) univariate polynomials
• Grassmann invariants, almost zeros and the determinantal zero, pole assignment problems of linear multivariable systems
• Generalized Resultant Theorem
• A matrix pencil based numerical method for the computation of the GCD of polynomials
• Resultant properties of gcd of many polynomials and a factorization representation of gcd
• Computation of the GCD of polynomials using gaussian transformations and shifting
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