Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F16%3A00467970" target="_blank" >RIV/67985807:_____/16:00467970 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/46747885:24510/16:00003940 RIV/00216208:11320/16:10331352

Výsledek na webu

<a href="http://dx.doi.org/10.1137/15M1028339" target="_blank" >http://dx.doi.org/10.1137/15M1028339</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/15M1028339" target="_blank" >10.1137/15M1028339</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense

Popis výsledku v původním jazyce

Recently it was shown how necessary and sufficient information for solving an orthogonally invariant linear approximation problem AX approx B with multiple right-hand sides can be revealed through the so-called core problem reduction; see [I. Hnětynková, M. Plešinger, and Z. Strakoš, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 917–931]. The total least squares (TLS) serves as an important example of such approximation problem. Solvability of TLS was discussed in the full generality in [I. Hnětynková et al., SIAM J. Matrix Anal. Appl., 32 (2011), pp. 748–770]. This theoretical study investigates solvability of core problems with multiple right-hand sides in the TLS sense. It is shown that, contrary to the single right-hand side case, a core problem with multiple right-hand sides may not have a TLS solution. Further possible internal structure of core problems is studied. Outputs of the classical TLS algorithm for the original problem AX approx B and for the core problem within AX approx B are compared.

Název v anglickém jazyce

Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense

Popis výsledku anglicky

Recently it was shown how necessary and sufficient information for solving an orthogonally invariant linear approximation problem AX approx B with multiple right-hand sides can be revealed through the so-called core problem reduction; see [I. Hnětynková, M. Plešinger, and Z. Strakoš, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 917–931]. The total least squares (TLS) serves as an important example of such approximation problem. Solvability of TLS was discussed in the full generality in [I. Hnětynková et al., SIAM J. Matrix Anal. Appl., 32 (2011), pp. 748–770]. This theoretical study investigates solvability of core problems with multiple right-hand sides in the TLS sense. It is shown that, contrary to the single right-hand side case, a core problem with multiple right-hand sides may not have a TLS solution. Further possible internal structure of core problems is studied. Outputs of the classical TLS algorithm for the original problem AX approx B and for the core problem within AX approx B are compared.

Druh

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

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

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

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

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

37

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

861-876

Kód UT WoS článku

000386451400003

EID výsledku v databázi Scopus

2-s2.0-84990847714