About: Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	The direct methods for the solution of systems of linear equations with a symmetric positive semidefinite matrix A usually comprise the Cholesky decomposition of a nonsingular diagonal block of A and effective evaluation of the action of a generalized inverse of the corresponding Schur complement. In this note we deal with both problems, paying special attention to the stiffness matrices of floating structures without mechanisms. We present a procedure which first identifies a well-conditioned positive definite diagonal block, then decomposes it by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S. The Schur complement is typically very small, so the generalized inverse can be effectively evaluated by the SVD. If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any ``epsilon'. Moreover, if the kernel of A is known, then the SVD can be replaced by effective regularization. The results of numerical experiments show that the proposed method is useful for effective implementation of the FETI based domain decomposition methods. The direct methods for the solution of systems of linear equations with a symmetric positive semidefinite matrix A usually comprise the Cholesky decomposition of a nonsingular diagonal block of A and effective evaluation of the action of a generalized inverse of the corresponding Schur complement. In this note we deal with both problems, paying special attention to the stiffness matrices of floating structures without mechanisms. We present a procedure which first identifies a well-conditioned positive definite diagonal block, then decomposes it by the Cholesky decomposition, and finally evaluates a generalized inverse of the Schur complement S. The Schur complement is typically very small, so the generalized inverse can be effectively evaluated by the SVD. If the rank of A or a lower bound on the nonzero eigenvalues of A are known, then the SVD can be implemented without any ``epsilon'. Moreover, if the kernel of A is known, then the SVD can be replaced by effective regularization. The results of numerical experiments show that the proposed method is useful for effective implementation of the FETI based domain decomposition methods. (en)
Title	Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure (en)
skos:prefLabel	Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure (en)
skos:notation	RIV/61989100:27240/11:86080658!RIV13-GA0-27240___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/07/0294), Z(MSM6198910027)
http://linked.open...iv/cisloPeriodika	88
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Dostál, Zdeněk Brzobohatý, Tomáš Markopoulos, Alexandros Kovář, Petr Kozubek, Tomáš
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	Vysoká škola báňská - Technická univerzita Ostrava / Fakulta elektrotechniky a informatiky
http://linked.open...dnocenehoVysledku	190258
http://linked.open...ai/riv/idVysledku	RIV/61989100:27240/11:86080658
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	domain decomposition; generalized inverse; semidefinite matrices; Cholesky decomposition (en)
http://linked.open.../riv/klicoveSlovo	domain decomposition Cholesky decomposition generalized inverse semidefinite matrices
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[058D5B1EB8D5]
http://linked.open...i/riv/nazevZdroje	INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	5 (xsd:int)
http://linked.open...cetTvurcuVysledku	5 (xsd:int)
http://linked.open...vavai/riv/projekt	Qualitative analysis of contact problems with friction and asymptotically optimal algorithms for their solution
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	5
http://linked.open...iv/tvurceVysledku	Brzobohatý, Tomáš Dostál, Zdeněk Kovář, Petr Kozubek, Tomáš Markopoulos, Alexandros
http://linked.open...ain/vavai/riv/wos	000295226800004
http://linked.open...n/vavai/riv/zamer	Výpočetně náročné počítačové simulace a optimalizace
issn	0029-5981
number of pages	17 (xsd:int)
http://bibframe.org/vocab/doi	10.1002/nme.3187
http://localhost/t...ganizacniJednotka	27240

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