TLS formulation and core reduction for problems with structured right-hand sides

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384756" target="_blank" >RIV/00216208:11320/18:10384756 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24510/18:00005482

Výsledek na webu

<a href="https://doi.org/10.1016/j.laa.2018.06.016" target="_blank" >https://doi.org/10.1016/j.laa.2018.06.016</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.laa.2018.06.016" target="_blank" >10.1016/j.laa.2018.06.016</a>

Jazyk výsledku

angličtina

Název v původním jazyce

TLS formulation and core reduction for problems with structured right-hand sides

Popis výsledku v původním jazyce

The total least squares (TLS) represents a popular data fitting approach for solving linear approximation problems Ax approximate to b (i.e., with a vector right-hand side) and AX approximate to B (i.e., with a matrix right-hand side) contaminated by errors. This paper introduces a generalization of TLS formulation to problems with structured right-hand sides. First, we focus on the case, where the right-hand side and consequently also the solution are tensors. We show that whereas the basic solvability result can be obtained directly by matricization of both tensors, generalization of the core problem reduction is more complicated. The core reduction allows to reduce mathematically the problem dimensions by removing all redundant and irrelevant data from the system matrix and the right-hand side. We prove that the core problems within the original tensor problem and its matricized counterpart are in general different. Then, we concentrate on problems with even more structured right-hand sides, where the same model A corresponds to a set of various tensor right-hand sides. Finally, relations between the matrix and tensor core problem are discussed.

Název v anglickém jazyce

TLS formulation and core reduction for problems with structured right-hand sides

Popis výsledku anglicky

The total least squares (TLS) represents a popular data fitting approach for solving linear approximation problems Ax approximate to b (i.e., with a vector right-hand side) and AX approximate to B (i.e., with a matrix right-hand side) contaminated by errors. This paper introduces a generalization of TLS formulation to problems with structured right-hand sides. First, we focus on the case, where the right-hand side and consequently also the solution are tensors. We show that whereas the basic solvability result can be obtained directly by matricization of both tensors, generalization of the core problem reduction is more complicated. The core reduction allows to reduce mathematically the problem dimensions by removing all redundant and irrelevant data from the system matrix and the right-hand side. We prove that the core problems within the original tensor problem and its matricized counterpart are in general different. Then, we concentrate on problems with even more structured right-hand sides, where the same model A corresponds to a set of various tensor right-hand sides. Finally, relations between the matrix and tensor core problem are discussed.

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

2018

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

555

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

25

Strana od-do

241-265

Kód UT WoS článku

000442065900015

EID výsledku v databázi Scopus

2-s2.0-85048767492