Show simple item record

dc.contributor.author
Kazeev, Vladimir
dc.contributor.author
Reichmann, Oleg
dc.contributor.author
Schwab, Christoph
dc.date.accessioned
2022-09-12T14:12:11Z
dc.date.available
2017-06-10T15:56:56Z
dc.date.available
2022-09-12T14:12:11Z
dc.date.issued
2013-06-01
dc.identifier.issn
0024-3795
dc.identifier.issn
1873-1856
dc.identifier.other
10.1016/j.laa.2013.01.009
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/65735
dc.description.abstract
We consider a class of multilevel matrices arising, for example, from the discretization of linear diffusion operators in a d-dimensional hypercube. We derive explicit representations of such matrices in the Tensor Train (TT) format, introduced recently for the non-linear low-parametric approximation of multi-dimensional vectors with the aim to handle the “curse of dimensionality”. We obtain sharp upper bounds on the TT ranks, which are linear or, when the diffusion tensor is semiseparable or quasi-separable, even sublinear in d (cf. the straightforward quadratic estimate). The use of the Quantized Tensor Train (QTT) decomposition allows to further reduce the number of parameters.
en_US
dc.language.iso
en
en_US
dc.publisher
Elsevier
en_US
dc.subject
Low-rank representation
en_US
dc.subject
Diffusion operator
en_US
dc.subject
Tensor Train (TT) and
en_US
dc.subject
Quantized Tensor Train (QTT) formats
en_US
dc.subject
Curse of dimensionality
en_US
dc.subject
Semiseparable matrices
en_US
dc.subject
Quasi-separable matrices
en_US
dc.title
Low-rank tensor structure of linear diffusion operators in the TT and QTT formats
en_US
dc.type
Journal Article
dc.date.published
2013-02-28
ethz.journal.title
Linear Algebra and its Applications
ethz.journal.volume
438
en_US
ethz.journal.issue
11
en_US
ethz.journal.abbreviated
Linear Algebra Appl.
ethz.pages.start
4204
en_US
ethz.pages.end
4221
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Amsterdam
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02501 - Seminar für Angewandte Mathematik / Seminar for Applied Mathematics::03435 - Schwab, Christoph / Schwab, Christoph
ethz.relation.isNewVersionOf
10.3929/ethz-a-010395841
ethz.date.deposited
2017-06-10T15:59:07Z
ethz.source
ECIT
ethz.identifier.importid
imp59365081bdacf89213
ethz.ecitpid
pub:104769
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.installDate
2017-07-18T08:33:43Z
ethz.rosetta.lastUpdated
2022-03-28T11:39:05Z
ethz.rosetta.exportRequired
true
ethz.rosetta.versionExported
true
ethz.COinS
ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.atitle=Low-rank%20tensor%20structure%20of%20linear%20diffusion%20operators%20in%20the%20TT%20and%20QTT%20formats&rft.jtitle=Linear%20Algebra%20and%20its%20Applications&rft.date=2013-06-01&rft.volume=438&rft.issue=11&rft.spage=4204&rft.epage=4221&rft.issn=0024-3795&1873-1856&rft.au=Kazeev,%20Vladimir&Reichmann,%20Oleg&Schwab,%20Christoph&rft.genre=article&rft_id=info:doi/10.1016/j.laa.2013.01.009&
 Search print copy at ETH Library

Files in this item

FilesSizeFormatOpen in viewer

There are no files associated with this item.

Publication type

Show simple item record