Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure
Original language 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 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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F07%2F0294" target="_blank" >GA201/07/0294: Qualitative analysis of contact problems with friction and asymptotically optimal algorithms for their solution</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
ISSN
0029-5981
e-ISSN
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Volume of the periodical
5
Issue of the periodical within the volume
88
Country of publishing house
GB - UNITED KINGDOM
Number of pages
17
Pages from-to
493-509
UT code for WoS article
000295226800004
EID of the result in the Scopus database
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