The Core Problem within a Linear Approximation Problem $AXapprox B$ with Multiple Right-Hand Sides
The result's identifiers
Result code in 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>
Alternative codes found
RIV/67985807:_____/13:00426569
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
The Core Problem within a Linear Approximation Problem $AXapprox B$ with Multiple Right-Hand Sides
Original language description
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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-06684S" target="_blank" >GA13-06684S: Iterative Methods in Computational Mathematics: Analysis, Preconditioning, and Applications</a><br>
Continuities
O - Projekt operacniho programu
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Matrix Analysis and Appliccations
ISSN
0895-4798
e-ISSN
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Volume of the periodical
34
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
917-931
UT code for WoS article
325092700004
EID of the result in the Scopus database
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