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dc.contributor.authorLee, Gyou-Bongen_US
dc.date.accessioned2014-03-14T21:21:21Z
dc.date.available2014-03-14T21:21:21Z
dc.date.issued1991-05-05en_US
dc.identifier.otheretd-10142005-135800en_US
dc.identifier.urihttp://hdl.handle.net/10919/39916
dc.description.abstract

The 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_US
dc.format.mediumBTDen_US
dc.publisherVirginia Techen_US
dc.relation.haspartLD5655.V856_1991.L437.pdfen_US
dc.subjectEigenvalues Researchen_US
dc.subjectConvergence Researchen_US
dc.subject.lccLD5655.V856 1991.L437en_US
dc.titleA study of the computation and convergence behavior of eigenvalue bounds for self-adjoint operatorsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10142005-135800/en_US
dc.date.sdate2005-10-14en_US
dc.date.rdate2005-10-14
dc.date.adate2005-10-14en_US


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