Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices

dc.contributor.advisor Dieci, Luca
dc.contributor.author Pugliese, Alessandro en_US
dc.contributor.committeeMember Chow, Shui-Nee
dc.contributor.committeeMember Liu, Yingjie
dc.contributor.committeeMember Loss, Michael
dc.contributor.committeeMember Verriest, Erik
dc.contributor.department Mathematics en_US
dc.date.accessioned 2008-09-17T19:32:47Z
dc.date.available 2008-09-17T19:32:47Z
dc.date.issued 2008-05-05 en_US
dc.description.abstract In this thesis, we consider real matrix functions that depend on two parameters and study the problem of how to detect and approximate parameters' values where the singular values coalesce. We prove several results connecting the existence of coalescing points to the periodic structure of the smooth singular values decomposition computed around the boundary of a domain enclosing the points. This is further used to develop algorithms for the detection and approximation of coalescing points in planar regions. Finally, we present techniques for continuing curves of coalescing singular values of matrices depending on three parameters, and illustrate how these techniques can be used to locate coalescing singular values of complex-valued matrices depending on three parameters. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/24730
dc.publisher Georgia Institute of Technology en_US
dc.subject Periodicity en_US
dc.subject Matrix function en_US
dc.subject Eigenvalues en_US
dc.subject Conical intersection en_US
dc.subject Singular values en_US
dc.subject.lcsh Eigenvalues
dc.subject.lcsh Matrices
dc.subject.lcsh Decomposition (Mathematics)
dc.subject.lcsh Algorithms
dc.subject.lcsh Eigenvectors
dc.subject.lcsh Differential operators
dc.title Theoretical and numerical aspects of coalescing of eigenvalues and singular values of parameter dependent matrices en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Dieci, Luca
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
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relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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