ON A SPARSE REPRESENTATION OF LAPLACIAN

Kód výsledku v 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>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

ON A SPARSE REPRESENTATION OF LAPLACIAN

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

ON A SPARSE REPRESENTATION OF LAPLACIAN

Popis výsledku anglicky

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

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

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

ACC Journal

ISSN

1803-9782

e-ISSN

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Svazek periodika

XVIII

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

6

Strana od-do

40-45

Kód UT WoS článku

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EID výsledku v databázi Scopus

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