ON THE PRECONDITIONED CONJUGATE GRADIENT METHOD FOR SOLVING (A minus lambda B)X equals 0.

Papadrakakis, Manolis; Yakoumidakis, Michalis

dc.contributor.author	Papadrakakis, Manolis	en
dc.contributor.author	Yakoumidakis, Michalis	en
dc.date.accessioned	2014-03-01T01:39:14Z
dc.date.available	2014-03-01T01:39:14Z
dc.date.issued	1987	en
dc.identifier.issn	00295981	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/22627
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-0023382065&partnerID=40&md5=f69a4a7a9d24ba217b6c7f7019c44d33	en
dc.subject.other	COMPUTER AIDED ANALYSIS	en
dc.subject.other	CONJUGATE GRADIENT METHOD	en
dc.subject.other	MATHEMATICAL TECHNIQUES	en
dc.title	ON THE PRECONDITIONED CONJUGATE GRADIENT METHOD FOR SOLVING (A minus lambda B)X equals 0.	en
heal.type	journalArticle	en
heal.publicationDate	1987	en
heal.abstract	Classical iterative methods when applied to the partial solution of the generalized eigenvalue problem Ax equals lambda Bx, may yield very poor convergence rates particularly when ill-conditioned problems are considered. In this paper the preconditioned conjugate gradient (CG) method via the minimization of the Rayleigh quotient and the reverse power method is employed for the partial eigenproblem. The triangular splitting preconditioners employed are obtained from an incomplete Choleski factorization and a partial Evans preconditioner. This approach can dramatically improve the convergence rate of the basic CG method and is applicable to any symmetric eigenproblem in which one of the matrices A,B is positive definite. 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 is likely to be very promising.	en
heal.journalName	International Journal for Numerical Methods in Engineering	en
dc.identifier.volume	24	en
dc.identifier.issue	7	en
dc.identifier.spage	1355	en
dc.identifier.epage	1366	en