About: Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://link.springer.com/chapter/10.1007/978-1-4614-7172-1_3
Description	Matrices of two-by-two block form with matrix blocks of equal order arise in various important applications, such as when solving complex-valued systems in real arithmetics, in linearized forms of the Cahn–Hilliard diffusive phase-field differential equation model and in constrained partial differential equations with distributed control. It is shown how an efficient preconditioner can be constructed which, under certain conditions, has a resulting spectral condition number of about 2. The preconditioner avoids the use of Schur complement matrices and needs only solutions with matrices that are linear combinations of the matrices appearing in each block row of the given matrix and for which often efficient preconditioners are already available. Matrices of two-by-two block form with matrix blocks of equal order arise in various important applications, such as when solving complex-valued systems in real arithmetics, in linearized forms of the Cahn–Hilliard diffusive phase-field differential equation model and in constrained partial differential equations with distributed control. It is shown how an efficient preconditioner can be constructed which, under certain conditions, has a resulting spectral condition number of about 2. The preconditioner avoids the use of Schur complement matrices and needs only solutions with matrices that are linear combinations of the matrices appearing in each block row of the given matrix and for which often efficient preconditioners are already available. (en)
Title	Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I (en)
skos:prefLabel	Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I Preconditioners for Some Matrices of Two-by-Two Block Form, with Applications, I (en)
skos:notation	RIV/68145535:_____/13:00397048!RIV14-MSM-68145535
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(ED1.1.00/02.0070)
http://linked.open...iv/cisloPeriodika	45
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Axelsson, Owe
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 geoniky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	98509
http://linked.open...ai/riv/idVysledku	RIV/68145535:_____/13:00397048
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	two-by-two block-structured matrices; preconditioning; complex-valued system; Cahn-Hilliard phase-field model; optimal control (en)
http://linked.open.../riv/klicoveSlovo	preconditioning optimal control Cahn-Hilliard phase-field model complex-valued system two-by-two block-structured matrices
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[BD1F732E48B3]
http://linked.open...i/riv/nazevZdroje	Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	IT4Innovations Centre of Excellence
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	45
http://linked.open...iv/tvurceVysledku	Axelsson, Owe
issn	2194-1009
number of pages	23 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/978-1-4614-7172-1_3

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