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

 
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1996 (EN)
Numerical performance of the matrix pencil algorithm computing the greatest common divisor of polynomials and comparison with other matrix-based methodologies (EN)

Mitrouli, M (EN)
Karcanias, N (EN)
Koukouvinos, C (EN)

N/A (EN)

This paper presents a new numerical algorithm for the computation of the greatest common divisor (GCD) of several polynomials, based on system-theoretic properties. The specific algorithm, characterizes the GCD as the output decoupling zero polynomial of an appropriate linear system associated with the given polynomial set. The computation of the GCD is thus reduced to specifying a nonzero entry of a vector forming the compound matrix of a matrix pencil directly produced from the associated linear system. A detailed description of the implementation of the algorithm is presented and analytical proofs of its stability are also developed. The MATLAB code of the algorithm is also described in the appendix. (EN)

journalArticle

Linear systems (EN)
Computational methods (EN)
Software package MATLAB (EN)
System theoretic properties (EN)
Matrix algebra (EN)
Vectors (EN)
Algorithms (EN)
Matrix pencil algorithm (EN)
Greatest common divisor of polynomials (EN)
Numerical algorithms (EN)
Output decoupling zero polynomial (EN)
Polynomials (EN)
Matrix pencils (EN)
Greatest common divisor (GCD) (EN)

Εθνικό Μετσόβιο Πολυτεχνείο (EL)
National Technical University of Athens (EN)

Journal of Computational and Applied Mathematics (EN)

1996


ELSEVIER SCIENCE BV (EN)



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