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

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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


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