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

Mitrouli, M; Karcanias, N; Koukouvinos, C

dc.contributor.author	Mitrouli, M	en
dc.contributor.author	Karcanias, N	en
dc.contributor.author	Koukouvinos, C	en
dc.date.accessioned	2014-03-01T01:12:08Z
dc.date.available	2014-03-01T01:12:08Z
dc.date.issued	1996	en
dc.identifier.issn	0377-0427	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/11966
dc.subject	Greatest common divisor of polynomials	en
dc.subject	Linear systems	en
dc.subject	Matrix pencils	en
dc.subject	Numerical algorithms	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Algorithms	en
dc.subject.other	Computational methods	en
dc.subject.other	Matrix algebra	en
dc.subject.other	Vectors	en
dc.subject.other	Greatest common divisor (GCD)	en
dc.subject.other	Matrix pencil algorithm	en
dc.subject.other	Output decoupling zero polynomial	en
dc.subject.other	Software package MATLAB	en
dc.subject.other	System theoretic properties	en
dc.subject.other	Polynomials	en
dc.title	Numerical performance of the matrix pencil algorithm computing the greatest common divisor of polynomials and comparison with other matrix-based methodologies	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0377-0427(96)00092-1	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0377-0427(96)00092-1	en
heal.language	English	en
heal.publicationDate	1996	en
heal.abstract	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
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Journal of Computational and Applied Mathematics	en
dc.identifier.doi	10.1016/S0377-0427(96)00092-1	en
dc.identifier.isi	ISI:A1996VZ45400006	en
dc.identifier.volume	76	en
dc.identifier.issue	1-2	en
dc.identifier.spage	89	en
dc.identifier.epage	112	en