On TLS formulation and core reduction for data fitting with generalized models
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10404455" target="_blank" >RIV/00216208:11320/19:10404455 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24510/19:00006481
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Pkg1OurZFf" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Pkg1OurZFf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2019.04.018" target="_blank" >10.1016/j.laa.2019.04.018</a>
Alternative languages
Result language
angličtina
Original language name
On TLS formulation and core reduction for data fitting with generalized models
Original language description
The total least squares (TLS) framework represents a popular data fitting approach for solving matrix approximation problems of the form A(X) a AX approximate to B. A general linear mapping on spaces of matrices A : X -> B can be represented by a fourth-order tensor which is in the AX approximate to B case highly structured. This has a direct impact on solvability of the corresponding TLS problem, which is known to be complicated. Thus this paper focuses on several generalizations of the model A: the bilinear model, the model of higher Kronecker rank, and the fully tensorized model. It is shown how the corresponding generalization of the TLS formulation induces enrichment of the search space for the data corrections. Solvability of the resulting minimization problem is studied. Furthermore, extension of the so-called core reduction to the bilinear model is presented. For the fully tensor model, its relation to a particular single right-hand side TLS problem is derived. Relationships among individual formulations are discussed. (C) 2019 Elsevier Inc. All rights reserved.
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
<a href="/en/project/GC17-04150J" target="_blank" >GC17-04150J: Reliable two-scale Fourier/finite element-based simulations: Error-control, model reduction, and stochastics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Linear Algebra and Its Applications
ISSN
0024-3795
e-ISSN
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Volume of the periodical
577
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
20
Pages from-to
1-20
UT code for WoS article
000474327200001
EID of the result in the Scopus database
2-s2.0-85064701229