dc.date.accessioned 2013-03-12T09:10:44Z dc.date.available 2013-03-12T09:10:44Z dc.date.issued 2011 en_US dc.date.submitted 2012-02-02 en_US dc.identifier.citation Jarlebring, Elias, , Kvaal, Simen, , Michiels, Wim, , . Computing all Pairs (λ,μ) Such That λ is a Double Eigenvalue of Α + μΒ. SIAM Journal on Matrix Analysis and Applications. 2011, 32, 902 en_US dc.identifier.uri http://hdl.handle.net/10852/12743 dc.description.abstract Double eigenvalues are not generic for matrices without any particular structure. A matrix depending linearly on a scalar parameter, Α + μΒ, will, however, generically have double eigenvalues for some values of the parameter μ. In this paper, we consider the problem of finding those values. More precisely, we construct a method to accurately find all scalar pairs (λ,μ) such that Α + μΒ has a double eigenvalue λ, where Α and Β are given arbitrary complex matrices. The general idea of the globally convergent method is that if μ is close to a solution, then Α + μΒ has two eigenvalues which are close to each other. We fix the relative distance between these two eigenvalues and construct a method to solve and study it by observing that the resulting problem can be stated as a two-parameter eigenvalue problem, which is already studied in the literature. The method, which we call the method of fixed relative distance (MFRD), involves solving a two-parameter eigenvalue problem which returns approximations of all solutions. It is unfortunately not possible to get full accuracy with MFRD. In order to compute solutions with full accuracy, we present an iterative method which returns a very accurate solution, for a sufficiently good starting value. The approach is illustrated with one academic example and one application to a simple problem in computational quantum mechanics. eng Copyright 2011 Society for Industrial and Applied Mathematics dc.language.iso eng en_US dc.title Computing all Pairs (λ,μ) Such That λ is a Double Eigenvalue of Α + μΒ en_US dc.type Journal article en_US dc.date.updated 2012-02-06 en_US dc.creator.author Jarlebring, Elias en_US dc.creator.author Kvaal, Simen en_US dc.creator.author Michiels, Wim en_US dc.subject.nsi VDP::440 en_US cristin.unitcode 151200 en_US cristin.unitname Kjemisk institutt en_US dc.identifier.cristin 893550 en_US dc.identifier.bibliographiccitation info:ofi/fmt:kev:mtx:ctx&ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM Journal on Matrix Analysis and Applications&rft.volume=32&rft.spage=902&rft.date=2011 en_US dc.identifier.jtitle SIAM Journal on Matrix Analysis and Applications dc.identifier.volume 32 dc.identifier.startpage 902 dc.identifier.endpage 927 dc.identifier.doi http://dx.doi.org/10.1137/100783157 dc.identifier.urn URN:NBN:no-30385 en_US dc.type.document Tidsskriftartikkel en_US dc.identifier.duo 150681 en_US dc.type.peerreviewed Peer reviewed en_US dc.identifier.fulltext Fulltext https://www.duo.uio.no/bitstream/handle/10852/12743/1/SIMAX_32_902.pdf dc.type.version PublishedVersion
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