THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10159151" target="_blank" >RIV/00216208:11320/13:10159151 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/120884237" target="_blank" >http://dx.doi.org/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 AX ~ B WITH MULTIPLE RIGHT-HAND SIDES

Popis výsledku v původním jazyce

This paper focuses on total least squares (TLS) problems AX ~ B with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnetynkova 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. Strakos, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861-875] showed how necessary and sufficient information for solving Ax ~ b can be revealed from the original data throughthe 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. Weshow 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-hand sides.

Název v anglickém jazyce

THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES

Popis výsledku anglicky

This paper focuses on total least squares (TLS) problems AX ~ B with multiple right-hand sides. Existence and uniqueness of a TLS solution for such problems was analyzed in the paper [I. Hnetynkova 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. Strakos, SIAM J. Matrix Anal. Appl., 27, 2006, pp. 861-875] showed how necessary and sufficient information for solving Ax ~ b can be revealed from the original data throughthe 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. Weshow 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-hand sides.

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/GA201%2F09%2F0917" target="_blank" >GA201/09/0917: Matematická a počítačová analýza evolučních procesů v nelineárních viskoelastických tekutinách</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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 Applications

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

000325092700004

EID výsledku v databázi Scopus

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