On Wavelet Matrix Compression for Differential Equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F11%3A%230000792" target="_blank" >RIV/46747885:24510/11:#0000792 - isvavai.cz</a>

Výsledek na webu

<a href="http://proceedings.aip.org/resource/2/apcpcs/1389/1/1574_1?isAuthorized=no" target="_blank" >http://proceedings.aip.org/resource/2/apcpcs/1389/1/1574_1?isAuthorized=no</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.3637931" target="_blank" >10.1063/1.3637931</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Wavelet Matrix Compression for Differential Equations

Popis výsledku v původním jazyce

The design of most adaptive wavelet methods for solving differential equations follows a general concept proposed by A. Cohen, W. Dahmen and R. DeVore in [5, 6]. The essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l2 problem, finding of the convergent iteration process for the l2 problem and finally derivation of its finite dimensional version which works with an inexact right hand side and approximate matrix-vector multiplication. In ourcontribution, we shortly review all these parts with emphasis on the approximate matrix-vector multiplication. Efficient approximation of matrix-vector multiplication is enabled by an off-diagonal decay of entries of the wavelet stiffness matrix and bydecay of entries of load vector in wavelet coordinates. Besides an usual truncation in scale, we apply here also a truncation in space to compress wavelet stiffness matrices efficiently. At the end, we show some numerical experiments.

Název v anglickém jazyce

On Wavelet Matrix Compression for Differential Equations

Popis výsledku anglicky

The design of most adaptive wavelet methods for solving differential equations follows a general concept proposed by A. Cohen, W. Dahmen and R. DeVore in [5, 6]. The essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l2 problem, finding of the convergent iteration process for the l2 problem and finally derivation of its finite dimensional version which works with an inexact right hand side and approximate matrix-vector multiplication. In ourcontribution, we shortly review all these parts with emphasis on the approximate matrix-vector multiplication. Efficient approximation of matrix-vector multiplication is enabled by an off-diagonal decay of entries of the wavelet stiffness matrix and bydecay of entries of load vector in wavelet coordinates. Besides an usual truncation in scale, we apply here also a truncation in space to compress wavelet stiffness matrices efficiently. At the end, we show some numerical experiments.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GP201%2F09%2FP641" target="_blank" >GP201/09/P641: Waveletové adaptivní metody se stabilními bázemi</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2011

Kód důvěrnosti údajů

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

Název statě ve sborníku

NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011

ISBN

978-0-7354-0956-9

ISSN

—

e-ISSN

—

Počet stran výsledku

4

Strana od-do

1574-1577

Název nakladatele

American Institute of Physics

Místo vydání

Melville, New York

Místo konání akce

Halkidiki, (Greece)

Datum konání akce

1. 1. 2011

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

302239800378