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Statements

Subject Item
n2:RIV%2F61989100%3A27240%2F11%3A86080658%21RIV13-GA0-27240___
rdf:type
n7:Vysledek skos:Concept
dcterms: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.
dcterms: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
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
skos:notation
RIV/61989100:27240/11:86080658!RIV13-GA0-27240___
n7:predkladatel
n19:orjk%3A27240
n3:aktivita
n14:Z n14:P
n3:aktivity
P(GA201/07/0294), Z(MSM6198910027)
n3:cisloPeriodika
88
n3:dodaniDat
n9:2013
n3:domaciTvurceVysledku
n6:8277621 n6:8606609 n6:5021391 n6:7294611 n6:7723318
n3:druhVysledku
n18:J
n3:duvernostUdaju
n17:S
n3:entitaPredkladatele
n12:predkladatel
n3:idSjednocenehoVysledku
190258
n3:idVysledku
RIV/61989100:27240/11:86080658
n3:jazykVysledku
n5:eng
n3:klicovaSlova
domain decomposition; generalized inverse; semidefinite matrices; Cholesky decomposition
n3:klicoveSlovo
n8:domain%20decomposition n8:generalized%20inverse n8:Cholesky%20decomposition n8:semidefinite%20matrices
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[058D5B1EB8D5]
n3:nazevZdroje
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
n3:obor
n21:BA
n3:pocetDomacichTvurcuVysledku
5
n3:pocetTvurcuVysledku
5
n3:projekt
n13:GA201%2F07%2F0294
n3:rokUplatneniVysledku
n9:2011
n3:svazekPeriodika
5
n3:tvurceVysledku
Markopoulos, Alexandros Dostál, Zdeněk Kozubek, Tomáš Brzobohatý, Tomáš Kovář, Petr
n3:wos
000295226800004
n3:zamer
n16:MSM6198910027
s:issn
0029-5981
s:numberOfPages
17
n15:doi
10.1002/nme.3187
n20:organizacniJednotka
27240