A partial preconditioned conjugate gradient method for large eigenproblems

Papadrakakis, M; Yakoumidakis, M

dc.contributor.author	Papadrakakis, M	en
dc.contributor.author	Yakoumidakis, M	en
dc.date.accessioned	2014-03-01T01:39:12Z
dc.date.available	2014-03-01T01:39:12Z
dc.date.issued	1987	en
dc.identifier.issn	00457825	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/22603
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0023346601&partnerID=40&md5=c31a7ed752b238b443cb20ad15860cb0	en
dc.subject.other	FINITE ELEMENT DISCRETIZATION	en
dc.subject.other	LARGE EIGENPROBLEMS	en
dc.subject.other	PARTIAL PRECONDITIONED CONJUGATE GRADIENT METHOD	en
dc.subject.other	PRECONDITIONED ITERATIVE METHOD	en
dc.subject.other	RAYLEIGH QUOTIENT	en
dc.subject.other	MATHEMATICAL TECHNIQUES	en
dc.title	A partial preconditioned conjugate gradient method for large eigenproblems	en
heal.type	journalArticle	en
heal.publicationDate	1987	en
heal.abstract	In this paper a preconditioned iterative method suitable for the solution of the generalized eigenvalue problem Ax = λBx is presented. The proposed method is suitable for the determination of extreme eigenvalues and their corresponding eigenvectors of large sparse eigenproblems derived from the finite element discretization method. The solution is obtained through the minimization of the Rayleigh quotient by a preconditioned conjugate gradient (CG) method. The proposed triangular splitting preconditioner combines Evans' SSOR preconditioner with a drop-off tolerance criterion and is called partial preconditioner (PPR). The PPR is attractive in a large FE framework because it is simple and can be implemented at the element level, as opposed to incomplete Choleski preconditioners, which require a sparse assembly. Because of the renewed interest in CG techniques for FE work on microprocessors and parallel computers it is believed that this improved approach to the generalized eigenvalue problem, through the minimization of the Rayleigh quotient, is likely to be very promising. © 1987.	en
heal.journalName	Computer Methods in Applied Mechanics and Engineering	en
dc.identifier.volume	62	en
dc.identifier.issue	2	en
dc.identifier.spage	195	en
dc.identifier.epage	207	en