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

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1137/120884237
Description	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 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-hand sides. 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 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-hand sides. (en)
Title	THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES (en)
skos:prefLabel	THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES THE CORE PROBLEM WITHIN A LINEAR APPROXIMATION PROBLEM AX ~ B WITH MULTIPLE RIGHT-HAND SIDES (en)
skos:notation	RIV/00216208:11320/13:10159151!RIV14-GA0-11320___
http://linked.open...avai/predkladatel	Matematicko-fyzikální fakulta
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/09/0917)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Strakoš, Zdeněk Hnětynková, Iveta
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	67080
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10159151
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	singular value decomposition; orthogonal regression; error-in-variables modeling; linear approximation problem; core problem; multiple right-hand sides; total least squares problem (en)
http://linked.open.../riv/klicoveSlovo	core problem error-in-variables modeling linear approximation problem total least squares problem orthogonal regression singular value decomposition multiple right-hand sides
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[31B179DE8D5A]
http://linked.open...i/riv/nazevZdroje	SIAM Journal on Matrix Analysis and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	34
http://linked.open...iv/tvurceVysledku	Strakoš, Zdeněk Hnětynková, Iveta Plesinger, Martin
http://linked.open...ain/vavai/riv/wos	000325092700004
issn	0895-4798
number of pages	15 (xsd:int)
http://bibframe.org/vocab/doi	10.1137/120884237
http://localhost/t...ganizacniJednotka	11320

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