Computation of the GCD of polynomials using gaussian transformations and shifting

DOI10.1080/00207179308922998zbMath0777.93053OpenAlexW2116318259MaRDI QIDQ5287932

Nicos Karcanias, Marilena Mitrouli

Publication date: 8 August 1993

Published in: International Journal of Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207179308922998

zbMATH Keywords

numerical methodgreatest common divisor

Mathematics Subject Classification ID

Multivariable systems, multidimensional control systems (93C35) Linear systems in control theory (93C05)

Related Items (19)

A compound matrix algorithm for the computation of the Smith form of a polynomial matrix ⋮ Numerical and Symbolical Methods for the GCD of Several Polynomials ⋮ Approximate least common multiple of several polynomials using the ERES division algorithm ⋮ On the zeros of blocked time-invariant systems ⋮ Structured matrix methods computing the greatest common divisor of polynomials ⋮ Approximate zero polynomials of polynomial matrices and linear systems ⋮ Normal factorisation of polynomials and computational issues. ⋮ Approximate polynomial GCD over integers ⋮ System theoretic based characterisation and computation of the least common multiple of a set of polynomials. ⋮ Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation ⋮ 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 ⋮ Unnamed Item ⋮ Numerical performance of the matrix pencil algorithm computing the greatest common divisor of polynomials and comparison with other matrix-based methodologies ⋮ Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials ⋮ Compound matrices: Properties, numerical issues and analytical computations ⋮ On the Computation of the GCD of 2-D Polynomials ⋮ Nearest common root of a set of polynomials: a structured singular value approach ⋮ The feedback invariant measures of distance to uncontrollability and unobservability

Cites Work

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• Rank and null space calculations using matrix decomposition without column interchanges
• Invariance properties, and characterization of the greatest common divisor of a set of polynomials
• Matrix Analysis
• Generalized Resultant Theorem
• Comparison of algorithms for calculation of g.c.d. of polynomials
• A New Version of the Euclidean Algorith

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