dc.date.accessioned | 2022-03-12T18:11:51Z | |
dc.date.available | 2022-03-12T18:11:51Z | |
dc.date.created | 2021-08-26T15:44:01Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Floater, Michael S. Manni, Carla Sande, Espen Speleers, Hendrik . Best low-rank approximations and Kolmogorov n-widths. SIAM Journal on Matrix Analysis and Applications. 2021, 42(1), 330-350 | |
dc.identifier.uri | http://hdl.handle.net/10852/92387 | |
dc.description.abstract | We relate the problem of best low-rank approximation in the spectral norm for a matrix $A$ to Kolmogorov $n$-widths and corresponding optimal spaces. We characterize all the optimal spaces for the image of the Euclidean unit ball under $A$, and we show that any orthonormal basis in an $n$-dimensional optimal space generates a best rank-$n$ approximation to $A$. We also present a simple and explicit construction to obtain a sequence of optimal $n$-dimensional spaces once an initial optimal space is known. This results in a variety of solutions to the best low-rank approximation problem and provides alternatives to the truncated singular value decomposition. This variety can be exploited to obtain best low-rank approximations with problem-oriented properties. | |
dc.language | EN | |
dc.title | Best low-rank approximations and Kolmogorov n-widths | |
dc.type | Journal article | |
dc.creator.author | Floater, Michael S. | |
dc.creator.author | Manni, Carla | |
dc.creator.author | Sande, Espen | |
dc.creator.author | Speleers, Hendrik | |
cristin.unitcode | 185,15,13,0 | |
cristin.unitname | Matematisk institutt | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.cristin | 1929050 | |
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=42&rft.spage=330&rft.date=2021 | |
dc.identifier.jtitle | SIAM Journal on Matrix Analysis and Applications | |
dc.identifier.volume | 42 | |
dc.identifier.issue | 1 | |
dc.identifier.startpage | 330 | |
dc.identifier.endpage | 350 | |
dc.identifier.doi | https://doi.org/10.1137/20M1355720 | |
dc.identifier.urn | URN:NBN:no-94981 | |
dc.type.document | Tidsskriftartikkel | |
dc.type.peerreviewed | Peer reviewed | |
dc.source.issn | 0895-4798 | |
dc.identifier.fulltext | Fulltext https://www.duo.uio.no/bitstream/handle/10852/92387/1/ellipsoid_rev.pdf | |
dc.type.version | AcceptedVersion | |