Solvability classes for core problems in matrix total least squares minimization

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dc.contributor.authorHnětynková, Iveta
dc.contributor.authorPlešinger, Martin
dc.contributor.authorŽáková, Jana
dc.date.accessioned2019-09-26T07:55:09Z
dc.date.available2019-09-26T07:55:09Z
dc.date.issued2019
dc.description.abstractLinear matrix approximation problems AX approximate to B are often solved by the total least squares minimization (TLS). Unfortunately, the TLS solution may not exist in general. The so-called core problem theory brought an insight into this effect. Moreover, it simplified the solvability analysis if B is of column rank one by extracting a core problem having always a unique TLS solution. However, if the rank of B is larger, the core problem may stay unsolvable in the TLS sense, as shown for the first time by Hnetynkova, Pleinger, and Sima (2016). Full classification of core problems with respect to their solvability is still missing. Here we fill this gap. Then we concentrate on the so-called composed (or reducible) core problems that can be represented by a composition of several smaller core problems. We analyze how the solvability class of the components influences the solvability class of the composed problem. We also show on an example that the TLS solvability class of a core problem may be in some sense improved by its composition with a suitably chosen component. The existence of irreducible problems in various solvability classes is discussed.cs
dc.format.extent26 strancs
dc.identifier.doi10.21136/AM.2019.0252-18
dc.identifier.urihttps://dspace.tul.cz/handle/15240/153784
dc.identifier.urihttps://link.springer.com/article/10.21136/AM.2019.0252-18
dc.language.isocscs
dc.publisherACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS, ZITNA 25, PRAHA 1, 115 67, CZECH REPUBLIC
dc.relation.ispartofAPPLICATIONS OF MATHEMATICS
dc.subjectlinear approximation problemcs
dc.subjectcore problem theorycs
dc.subjecttotal least squarescs
dc.subjectclassificationcs
dc.subject(ir)reducible problemcs
dc.titleSolvability classes for core problems in matrix total least squares minimizationcs
local.citation.epage128
local.citation.spage103
local.event.edate2018-06-29
local.event.locationHejnice, CZECH REPUBLIC
local.event.sdate2018-06-24
local.event.title19th Conference on Programs and Algorithms of Numerical Mathematics (PANM)
local.identifier.publikace6147
local.relation.issue2
local.relation.volume64
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