Numerical performance of the matrix pencil algorithm computing the greatest common divisor of polynomials and comparison with other matrix-based methodologies

DOI10.1016/S0377-0427(96)00092-1zbMath0866.65013OpenAlexW1989356517MaRDI QIDQ5961649

Nicos Karcanias, Marilena Mitrouli, Christos Koukouvinos

Publication date: 13 July 1997

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(96)00092-1

zbMATH Keywords

algorithmstabilitygreatest common divisorpolynomialsimplementation

Mathematics Subject Classification ID

Polynomials in real and complex fields: factorization (12D05) Computation of special functions and constants, construction of tables (65D20)

Related Items

Approximate least common multiple of several polynomials using the ERES division algorithm ⋮ Normal factorisation of polynomials and computational issues. ⋮ Computing the polynomial remainder sequence via Bézout matrices ⋮ Blind image deconvolution via Hankel based method for computing the GCD of polynomials ⋮ Matrix pencil methodologies for computing the greatest common divisor of polynomials: hybrid algorithms and their performance ⋮ Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials ⋮ On rank and null space computation of the generalized Sylvester matrix

Uses Software

• Matlab

Cites Work

• Rank and null space calculations using matrix decomposition without column interchanges
• Fast projection methods for minimal design problems in linear system theory
• 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
• Computation of the GCD of polynomials using gaussian transformations and shifting
• Comparison of algorithms for calculation of g.c.d. of polynomials
• A New Version of the Euclidean Algorith
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