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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 -&gt; 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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • 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

  • 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