A study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operators

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dc.contributor.authorLee, Gyou-Bongen
dc.contributor.committeechairBeattie, Christopher A.en
dc.contributor.committeememberBurns, John A.en
dc.contributor.committeememberHannsgen, Kenneth B.en
dc.contributor.committeememberKim, J.U.en
dc.contributor.committeememberKohler, Werneren
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:21:21Zen
dc.date.adate2005-10-14en
dc.date.available2014-03-14T21:21:21Zen
dc.date.issued1991-05-05en
dc.date.rdate2005-10-14en
dc.date.sdate2005-10-14en
dc.description.abstractThe convergence rates for the method of Weinstein and a variant method of Aronszajn known as "truncation including the remainder" are derived in terms of the containment gaps between exact and approximating subspaces, using analytical techniques that arise in part in the convergence analysis of finite element methods for differential eigenvalue problems. An example of a one dimensional Schrodinger operator with a potential is presented which arises in quantum mechanics. Examples using the recent eigenvector-free (EVF) method of Beattie and Goerisch are considered. Since the EVF method uses finite element trial functions as approximating vectors, it produces sparse and well-structured coefficient matrices. For these large-order sparse matrix eigenvalue problems, we adapt a spectral transformation Lanczos algorithm for finding a few wanted eigenvalues. For a few particular examples of vibration in beams and plates, convergence behavior is experimentally evaluated.en
dc.description.degreePh. D.en
dc.format.extentvi, 92 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10142005-135800en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10142005-135800/en
dc.identifier.urihttp://hdl.handle.net/10919/39916en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1991.L437.pdfen
dc.relation.isformatofOCLC# 24362530en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1991.L437en
dc.subject.lcshConvergence -- Researchen
dc.subject.lcshEigenvalues -- Researchen
dc.titleA study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operatorsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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