About: Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Uvažujme ortogonálně invariantní lineární aproximační problém Ax~ b. C.C. Paige a Z. Strakoš dokázali, že částečná horní bidiagonalizace matice [b,A] vede na tzv. core aproximační problém, který obsahuje nutné a postačující informace pro řešení původní úlohy. I. Hnětynková a Z. Strakoš odvodili vlastnosti core problému ze vztahů mezi Lanczošovou třídiagonalizací a Golub-Kahanovou bidiagonalizací. V tomto příspěvku stručně připomeneme tento postup a nastíníme možné směry dalšího výzkumu. (cs) Consider an orthogonally invariant linear approximation problem Ax ~ b. C.C. Paige and Z. Strakoš proved that the partial upper bidiagonalization of the matrix [b,A] determines a core approximation problem that contains all necessary and sufficient information for solving the original problem. I. Hnětynková and Z. Strakoš derived the core problem formulation from the relationship between the Golub-Kahan bidiagonalization and the Lanczos tridiagonalization. Here we briefly recall this approach and outline a possible direction for further research. Consider an orthogonally invariant linear approximation problem Ax ~ b. C.C. Paige and Z. Strakoš proved that the partial upper bidiagonalization of the matrix [b,A] determines a core approximation problem that contains all necessary and sufficient information for solving the original problem. I. Hnětynková and Z. Strakoš derived the core problem formulation from the relationship between the Golub-Kahan bidiagonalization and the Lanczos tridiagonalization. Here we briefly recall this approach and outline a possible direction for further research. (en)
Title	Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem Lanczošova třídiagonalizace, Golub-Kahanova bidiagonalizace a core problém (cs) Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem (en)
skos:prefLabel	Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem Lanczošova třídiagonalizace, Golub-Kahanova bidiagonalizace a core problém (cs) Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem (en)
skos:notation	RIV/67985807:_____/06:00038852!RIV07-AV0-67985807
http://linked.open.../vavai/riv/strany	717;718
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1ET400300415), Z(AV0Z10300504)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2007
http://linked.open...aciTvurceVysledku	Strakoš, Zdeněk Hnětynková, Iveta Plešinger, Martin
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	Ústav informatiky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	482863
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/06:00038852
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	linear approximation problem; core problem; Golub-Kahan bidiagonalization; Lanczos tridiagonalization; Jacobi matrix; ill-posed problem (en)
http://linked.open.../riv/klicoveSlovo	core problem linear approximation problem Jacobi matrix Golub-Kahan bidiagonalization ill-posed problem Lanczos tridiagonalization
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[B235255449F2]
http://linked.open...i/riv/nazevZdroje	Proceedings in Applied Mathematics and Mechanics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Modelling and simulation of complex technical problems:effective numerical algorithms and parallel implementation using new information technologie
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	6
http://linked.open...iv/tvurceVysledku	Strakoš, Zdeněk Plešinger, Martin Hnětynková, Iveta
http://linked.open...n/vavai/riv/zamer	Informatika pro informační společnost: modely, algoritmy, aplikace
issn	1617-7061
number of pages	2 (xsd:int)
is http://linked.open...avai/riv/vysledek of	Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem Lanczos Tridiagonalization, Golub-Kahan Bidiagonalization and Core Problem

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