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dc.contributor.author
Parlett, Beresford N.
dc.contributor.author
Vömel, Christof
dc.date.accessioned
2017-06-10T17:18:28Z
dc.date.available
2017-06-10T17:18:28Z
dc.date.issued
2009-11
dc.identifier.issn
1064-8275
dc.identifier.issn
1095-7197
dc.identifier.other
10.1137/09077624X
dc.identifier.uri
http://hdl.handle.net/20.500.11850/67165
dc.description.abstract
A normalized eigenvector, or, more interestingly, an invariant subspace, is localized if its significant entries are defined by just part(s) of the matrix and negligible elsewhere. This paper presents two new procedures to detect such localization in eigenvectors of a symmetric tridiagonal matrix. The procedures are intended for use before the actual eigenvector computation. If localization is found, one may reduce costs by computing the vectors just from the relevant matrix regions. Practical eigensolvers from numerical libraries such as LAPACK and ScaLAPACK already inspect a given tridiagonal $T$ for off-diagonal entries that are of small magnitude relative to the matrix norm. These so-called splitting points indicate that $T$ breaks into smaller blocks, each one defining a subset of eigenvalues and localized eigenvectors. However, localization can occur even when none of the off-diagonals is particularly small. Our study investigates this more complicated phenomenon in the context of invariant subspaces belonging to isolated eigenvalue clusters.
dc.language.iso
en
dc.publisher
Society for Industrial and Applied Mathematics
dc.title
Detecting Localization in an Invariant Subspace
dc.type
Report
ethz.journal.title
SIAM Journal on Scientific Computing
ethz.journal.volume
33
ethz.journal.issue
6
ethz.journal.abbreviated
SIAM j. sci. comput.
ethz.pages.start
3447
ethz.pages.end
3467
ethz.notes
.
ethz.identifier.nebis
000018063
ethz.publication.place
Philadelphia, PA, USA
ethz.publication.status
published
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich, direkt::00012 - Lehre und Forschung, direkt::00007 - Departemente, direkt::02150 - Departement Informatik / Department of Computer Science
ethz.date.deposited
2017-06-10T17:19:28Z
ethz.source
ECIT
ethz.identifier.importid
imp593650a06b61274379
ethz.ecitpid
pub:106962
ethz.eth
yes
ethz.availability
Metadata only
ethz.rosetta.installDate
2017-07-12T18:11:55Z
ethz.rosetta.lastUpdated
2018-03-01T06:51:42Z
ethz.rosetta.versionExported
true
ethz.COinS
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