Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense
The result's identifiers
Result code in 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>
Alternative codes found
RIV/46747885:24510/16:00003940 RIV/00216208:11320/16:10331352
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Solvability of the Core Problem with Multiple Right-Hand Sides in the TLS Sense
Original language description
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.
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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
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 Applications
ISSN
0895-4798
e-ISSN
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Volume of the periodical
37
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
16
Pages from-to
861-876
UT code for WoS article
000386451400003
EID of the result in the Scopus database
2-s2.0-84990847714