About: Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We develop a general convergence theory for the generalized minimal residual method preconditioned by inner iterations for solving least squares problems. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory improves previous work [K. Morikuni and K. Hayami, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 1--22], particularly in the rank-deficient case. We also characterize the spectrum of the preconditioned coefficient matrix by the spectral radius of the iteration matrix for the inner iterations and give a convergence bound for the proposed methods. Finally, numerical experiments show that the proposed methods are more robust and efficient compared to previous methods for some rank-deficient problems. We develop a general convergence theory for the generalized minimal residual method preconditioned by inner iterations for solving least squares problems. The inner iterations are performed by stationary iterative methods. We also present theoretical justifications for using specific inner iterations such as the Jacobi and SOR-type methods. The theory improves previous work [K. Morikuni and K. Hayami, SIAM J. Matrix Anal. Appl., 34 (2013), pp. 1--22], particularly in the rank-deficient case. We also characterize the spectrum of the preconditioned coefficient matrix by the spectral radius of the iteration matrix for the inner iterations and give a convergence bound for the proposed methods. Finally, numerical experiments show that the proposed methods are more robust and efficient compared to previous methods for some rank-deficient problems. (en)
Title	Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems (en)
skos:prefLabel	Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems Convergence of Inner-Iteration GMRES Methods for Rank-Deficient Least Squares Problems (en)
skos:notation	RIV/67985807:_____/15:00438625!RIV15-AV0-67985807
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Morikuni, Keiichi
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	85
http://linked.open...ai/riv/idVysledku	RIV/67985807:_____/15:00438625
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	least squares problem; iterative methods; preconditioner; inner-outer iteration; GMRES method; stationary iterative method; rank-deficient problem (en)
http://linked.open.../riv/klicoveSlovo	inner-outer iteration least squares problem preconditioner rank-deficient problem stationary iterative method GMRES method iterative methods
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[9C1E20C22713]
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	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2015
http://linked.open...v/svazekPeriodika	36
http://linked.open...iv/tvurceVysledku	Hayami, K. Morikuni, Keiichi
issn	0895-4798
number of pages	26 (xsd:int)
http://bibframe.org/vocab/doi	10.1137/130946009

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