Numerical and Symbolical Methods for the GCD of Several Polynomials

DOI10.1007/978-94-007-0602-6_7zbMath1255.65062OpenAlexW59802204MaRDI QIDQ2913160

Dimitrios Christou, Dimitrios Triantafyllou, Nicos Karcanias, Marilena Mitrouli

Publication date: 26 September 2012

Published in: Lecture Notes in Electrical Engineering (Search for Journal in Brave)

Full work available at URL: https://openaccess.city.ac.uk/id/eprint/7300/1/%28232%29%20Book%20Chapter%20Springer%20Series%202011%2010-07-08.pdf

zbMATH Keywords

singular value decompositiongreatest common divisorGaussian eliminationresultantsymbolic-numeric computationsmatrix-pencil

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Polynomials, factorization in commutative rings (13P05)

Related Items

A hybrid method for computing the intersection and tangency points of plane curves ⋮ Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials

Uses Software

• MultRoot
• ERES

Cites Work

• An efficient and reliable algorithm for computing the singular subspace of a matrix, associated with its smallest singular values
• Approximate GCD and its application to ill-conditioned algebraic equations
• Linear multivariable control. A geometric approach
• An algorithm for computing certified approximate GCD of \(n\) univariate polynomials
• Certified approximate univariate GCDs
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• A new source of structured singular value decomposition problems
• Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation
• Computing greatest common divisors and squarefree decompositions through matrix methods: the parametric and approximate cases
• Invariance properties, and characterization of the greatest common divisor of a set of polynomials
• Greatest common divisors from generalized sylvester resultant matrices
• 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
• The approximate GCD of inexact polynomials
• Computation of the GCD of polynomials using gaussian transformations and shifting
• Matrix pencil methodologies for computing the greatest common divisor of polynomials: hybrid algorithms and their performance
• Comparison of algorithms for calculation of g.c.d. of polynomials
• Numerical Analysis and Its Applications
• Estimation of the Greatest Common Divisor of many polynomials using hybrid computations performed by the ERES method
• A New Version of the Euclidean Algorith
• Numerical computation of the least common multiple of a set of polynomials
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