On TLS formulation and core reduction for data fitting with generalized models

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/46747885:24510/19:00006481

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On TLS formulation and core reduction for data fitting with generalized models

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On TLS formulation and core reduction for data fitting with generalized models

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GC17-04150J" target="_blank" >GC17-04150J: Robustní dvojúrovňové simulace založené na Fourierově metodě a metodě konečných prvků: Odhady chyb, redukované modely a stochastika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Linear Algebra and Its Applications

ISSN

0024-3795

e-ISSN

—

Svazek periodika

577

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

20

Strana od-do

1-20

Kód UT WoS článku

000474327200001

EID výsledku v databázi Scopus

2-s2.0-85064701229