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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F11%3A86080658" target="_blank" >RIV/61989100:27240/11:86080658 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1002/nme.3187" target="_blank" >http://dx.doi.org/10.1002/nme.3187</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/nme.3187" target="_blank" >10.1002/nme.3187</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 positivedefinite 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 theSVD. 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. Th

Název v anglickém jazyce

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

Popis výsledku anglicky

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 positivedefinite 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 theSVD. 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. Th

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F07%2F0294" target="_blank" >GA201/07/0294: Kvalitativní analýza kontaktních úloh se třením a asymptoticky optimální algoritmy pro jejich řešení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

ISSN

0029-5981

e-ISSN

—

Svazek periodika

5

Číslo periodika v rámci svazku

88

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

17

Strana od-do

493-509

Kód UT WoS článku

000295226800004

EID výsledku v databázi Scopus

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