The Core Problem within a Linear Approximation Problem $AXapprox B$ with Multiple Right-Hand Sides

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F13%3A%230000992" target="_blank" >RIV/46747885:24510/13:#0000992 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/13:00426569

Výsledek na webu

<a href="http://epubs.siam.org/doi/abs/10.1137/120884237" target="_blank" >http://epubs.siam.org/doi/abs/10.1137/120884237</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/120884237" target="_blank" >10.1137/120884237</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Core Problem within a Linear Approximation Problem $AXapprox B$ with Multiple Right-Hand Sides

Popis výsledku v původním jazyce

This paper focuses on total least squares (TLS) problems $AXapprox B$ with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnětynková et al., SIAM J. Matrix Anal. Appl., 32, 2011, pp.748--770]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakoš, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861--875] showed how necessary and sufficient information for solving $Axapprox b$ can be revealed from the originaldata through the so-called core problem concept. In this paper we present a theoretical study extending this concept to problems with multiple right-hand sides. The data reduction we present here is based on the singular value decomposition of the system matrix $A$. We show minimality of the reduced problem; in this sense the situation is analogous to the single right-hand side case. Some other properties of the core problem, however, cannot be extended to the case of multiple right-han

Název v anglickém jazyce

The Core Problem within a Linear Approximation Problem $AXapprox B$ with Multiple Right-Hand Sides

Popis výsledku anglicky

This paper focuses on total least squares (TLS) problems $AXapprox B$ with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnětynková et al., SIAM J. Matrix Anal. Appl., 32, 2011, pp.748--770]. For TLS problems with single right-hand sides the paper [C. C. Paige and Z. Strakoš, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861--875] showed how necessary and sufficient information for solving $Axapprox b$ can be revealed from the originaldata through the so-called core problem concept. In this paper we present a theoretical study extending this concept to problems with multiple right-hand sides. The data reduction we present here is based on the singular value decomposition of the system matrix $A$. We show minimality of the reduced problem; in this sense the situation is analogous to the single right-hand side case. Some other properties of the core problem, however, cannot be extended to the case of multiple right-han

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA13-06684S" target="_blank" >GA13-06684S: Iterační metody ve výpočetní matematice: Analýza, předpodmínění a aplikace</a><br>

Návaznosti

O - Projekt operacniho programu

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Matrix Analysis and Appliccations

ISSN

0895-4798

e-ISSN

—

Svazek periodika

34

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

917-931

Kód UT WoS článku

325092700004

EID výsledku v databázi Scopus

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