ON A SPARSE REPRESENTATION OF LAPLACIAN

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F12%3A%230000805" target="_blank" >RIV/46747885:24510/12:#0000805 - isvavai.cz</a>
Result on the web
<a href="http://acc-ern.tul.cz/images/journal/sbornik/ACC_Journal_4_2012.pdf" target="_blank" >http://acc-ern.tul.cz/images/journal/sbornik/ACC_Journal_4_2012.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
ON A SPARSE REPRESENTATION OF LAPLACIAN
Original language description
One of the most important part of adaptive wavelet methods is an efficient approximate multiplication of stiffness matrices with vectors in wavelet coordinates. Although there are known algorithms to perform it in linear complexity, the application of them is relatively time consuming and its implementation is very difficult. Therefore, it is necessary to develop a wellconditioned wavelet basis with respect to which both the mass and stiffness matrices are sparse in the sense that the number of nonzeroelements in any column is bounded by a constant. Then, matrix-vector multiplication can be performed exactly with linear complexity. We present here a wavelet basis on the interval with respect to which both the mass and stiffness matrices correspondingto the one-dimensional Laplacian are sparse. Consequently, the stiffness matrix corresponding to the n-dimensional Laplacian in tensor product wavelet basis is also sparse. Moreover, the constructed basis has an excellent condition number
Czech name
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Czech description
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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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Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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