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dc.creatorSzyld, DB
dc.creatorXue, F
dc.date.accessioned2021-02-03T16:40:44Z
dc.date.available2021-02-03T16:40:44Z
dc.date.issued2016-01-01
dc.identifier.issn0025-5718
dc.identifier.issn1088-6842
dc.identifier.doihttp://dx.doi.org/10.34944/dspace/5731
dc.identifier.otherDT1WT (isidoc)
dc.identifier.urihttp://hdl.handle.net/20.500.12613/5749
dc.description.abstract© 2016 American Mathematical Society. Efficient computation of extreme eigenvalues of large-scale linear Hermitian eigenproblems can be achieved by preconditioned conjugate gradient (PCG) methods. In this paper, we study PCG methods for computing extreme eigenvalues of nonlinear Hermitian eigenproblems of the form T(λ)v = 0 that admit a nonlinear variational principle. We investigate some theoretical properties of a basic CG method, including its global and asymptotic convergence. We propose several variants of single-vector and block PCG methods with de- flation for computing multiple eigenvalues, and compare them in arithmetic and memory cost. Variable indefinite preconditioning is shown to be effective to accelerate convergence when some desired eigenvalues are not close to the lowest or highest eigenvalue. The efficiency of variants of PCG is illustrated by numerical experiments. Overall, the locally optimal block preconditioned conjugate gradient (LOBPCG) is the most efficient method, as in the linear setting.
dc.format.extent2887-2918
dc.language.isoen
dc.relation.haspartMathematics of Computation
dc.relation.isreferencedbyAmerican Mathematical Society (AMS)
dc.subjectNonlinear Hermitian eigenproblems
dc.subjectvariational principle
dc.subjectpreconditioned conjugate gradient
dc.subjectconvergence analysis
dc.titlePreconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. extreme eigenvalues
dc.typeArticle
dc.type.genreJournal Article
dc.relation.doi10.1090/mcom/3083
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.creator.orcidSzyld, Daniel B.|0000-0001-8010-0391
dc.date.updated2021-02-03T16:40:41Z
refterms.dateFOA2021-02-03T16:40:45Z


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