Matrix-Vector Multiplication in Adaptive Wavelet Methods

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F11%3A%230000787" target="_blank" >RIV/46747885:24510/11:#0000787 - isvavai.cz</a>

Výsledek na webu

<a href="http://proceedings.aip.org/resource/2/apcpcs/1410/1/147_1?isAuthorized=no" target="_blank" >http://proceedings.aip.org/resource/2/apcpcs/1410/1/147_1?isAuthorized=no</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.3664365" target="_blank" >10.1063/1.3664365</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Matrix-Vector Multiplication in Adaptive Wavelet Methods

Popis výsledku v původním jazyce

Wavelet based methods are an established tool in signal and image processing and a promising tool for the numerical solution of operator equations. They have namely some interesting properties which may provide an advantage over classical methods. It iswell-known fact that representations of smooth functions and also representations of a wide class of operators are sparse in wavelet coordinates. Further advantage of wavelet methods consists in the existence of a diagonal preconditioner. The condition number of the preconditioned stiffness matrices does not depend on the size of matrices. Although the stiffness matrices in wavelet coordinates are only quasi sparse, an approximate multiplication of these matrices with given sparse vectors can be performed in the linear complexity. These are crucial parts to design efficient adaptive wavelet schemes. In this contribution, we focus on biorthogonal spline wavelets and we compare different approximate matrix-vector multiplication techniques

Název v anglickém jazyce

Matrix-Vector Multiplication in Adaptive Wavelet Methods

Popis výsledku anglicky

Wavelet based methods are an established tool in signal and image processing and a promising tool for the numerical solution of operator equations. They have namely some interesting properties which may provide an advantage over classical methods. It iswell-known fact that representations of smooth functions and also representations of a wide class of operators are sparse in wavelet coordinates. Further advantage of wavelet methods consists in the existence of a diagonal preconditioner. The condition number of the preconditioned stiffness matrices does not depend on the size of matrices. Although the stiffness matrices in wavelet coordinates are only quasi sparse, an approximate multiplication of these matrices with given sparse vectors can be performed in the linear complexity. These are crucial parts to design efficient adaptive wavelet schemes. In this contribution, we focus on biorthogonal spline wavelets and we compare different approximate matrix-vector multiplication techniques

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

APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '11)

ISBN

978-0-7354-0984-2

ISSN

—

e-ISSN

—

Počet stran výsledku

395

Strana od-do

147-154

Název nakladatele

American Institute of Physics

Místo vydání

Melville, New York

Místo konání akce

Sozopol, Bulgaria

Datum konání akce

1. 1. 2011

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

301975000015