Krylov subspace approach to core problems within multilinear approximation problems: A unifying framework
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F23%3A00010098" target="_blank" >RIV/46747885:24510/23:00010098 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/23:10468019
Result on the web
<a href="https://epubs.siam.org/doi/abs/10.1137/21M1462155" target="_blank" >https://epubs.siam.org/doi/abs/10.1137/21M1462155</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1462155" target="_blank" >10.1137/21M1462155</a>
Alternative languages
Result language
angličtina
Original language name
Krylov subspace approach to core problems within multilinear approximation problems: A unifying framework
Original language description
Error contaminated linear approximation problems appear in a large variety of applications. The presence of redundant or irrelevant data complicates their solution. It was shown that such data can be removed by the core reduction yielding a minimally dimensioned subproblem called the core problem. Direct (SVD or Tucker decomposion-based) reduction has been introduced previously for problems with matrix models and vector, or matrix, or tensor observations; and also for problems with bilinear models. For the cases of vector and matrix observations a Krylov subspace method, the generalized Golub--Kahan bidiagonalization, can be used to extract the core problem. In this paper, we first unify previously studied variants of linear approximation problems under the general framework of multilinear approximation problem. We show how the direct core reduction can be extended to it. Then we show that the generalized Golub--Kahan bidiagonalization yields the core problem for any multilinear approximation problem. This further allows to prove various properties of core problems, in particular we give upper bounds on the multiplicity of singular values of reduced matrices.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM journal on matrix analysis and applications
ISSN
0895-4798
e-ISSN
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Volume of the periodical
44
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
26
Pages from-to
53-79
UT code for WoS article
000974412700001
EID of the result in the Scopus database
2-s2.0-85151047636