TLS formulation and core reduction for problems with structured right-hand sides

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384756" target="_blank" >RIV/00216208:11320/18:10384756 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24510/18:00005482
Result on the web
<a href="https://doi.org/10.1016/j.laa.2018.06.016" target="_blank" >https://doi.org/10.1016/j.laa.2018.06.016</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2018.06.016" target="_blank" >10.1016/j.laa.2018.06.016</a>

Result language
angličtina
Original language name
TLS formulation and core reduction for problems with structured right-hand sides
Original language description
The total least squares (TLS) represents a popular data fitting approach for solving linear approximation problems Ax approximate to b (i.e., with a vector right-hand side) and AX approximate to B (i.e., with a matrix right-hand side) contaminated by errors. This paper introduces a generalization of TLS formulation to problems with structured right-hand sides. First, we focus on the case, where the right-hand side and consequently also the solution are tensors. We show that whereas the basic solvability result can be obtained directly by matricization of both tensors, generalization of the core problem reduction is more complicated. The core reduction allows to reduce mathematically the problem dimensions by removing all redundant and irrelevant data from the system matrix and the right-hand side. We prove that the core problems within the original tensor problem and its matricized counterpart are in general different. Then, we concentrate on problems with even more structured right-hand sides, where the same model A corresponds to a set of various tensor right-hand sides. Finally, relations between the matrix and tensor core problem are discussed.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GC17-04150J" target="_blank" >GC17-04150J: Reliable two-scale Fourier/finite element-based simulations: Error-control, model reduction, and stochastics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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