Wavelet Bases on the Interval with Short Support and Vanishing Moments

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F12%3A%230000825" target="_blank" >RIV/46747885:24510/12:#0000825 - isvavai.cz</a>

Výsledek na webu

<a href="http://proceedings.aip.org/resource/2/apcpcs/1497/1/126_1?isAuthorized=no" target="_blank" >http://proceedings.aip.org/resource/2/apcpcs/1497/1/126_1?isAuthorized=no</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.4766776" target="_blank" >10.1063/1.4766776</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Wavelet Bases on the Interval with Short Support and Vanishing Moments

Popis výsledku v původním jazyce

Jia and Zhao have recently proposed a construction of a cubic spline wavelet basis on the interval which satisfies homogeneous Dirichlet boundary conditions of the second order. They used the basis for solving fourth order problems and they showed that Galerkin method with this basis has superb convergence. The stiffness matrices for the biharmonic equation defined on a unit square have very small and uniformly bounded condition numbers. In our contribution, we design wavelet bases with the same scalingfunctions and different wavelets. We show that our basis has the same quantitative properties as the wavelet basis constructed by Jia and Zhao and additionally the wavelets have vanishing moments. It enables to use this wavelet basis in adaptive waveletmethods and non-adaptive sparse grid methods. Furthermore, we even improve the condition numbers of the stiffness matrices by including lower levels.

Název v anglickém jazyce

Wavelet Bases on the Interval with Short Support and Vanishing Moments

Popis výsledku anglicky

Jia and Zhao have recently proposed a construction of a cubic spline wavelet basis on the interval which satisfies homogeneous Dirichlet boundary conditions of the second order. They used the basis for solving fourth order problems and they showed that Galerkin method with this basis has superb convergence. The stiffness matrices for the biharmonic equation defined on a unit square have very small and uniformly bounded condition numbers. In our contribution, we design wavelet bases with the same scalingfunctions and different wavelets. We show that our basis has the same quantitative properties as the wavelet basis constructed by Jia and Zhao and additionally the wavelets have vanishing moments. It enables to use this wavelet basis in adaptive waveletmethods and non-adaptive sparse grid methods. Furthermore, we even improve the condition numbers of the stiffness matrices by including lower levels.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

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 statě ve sborníku

APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12)

ISBN

978-0-7354-1111-1

ISSN

—

e-ISSN

—

Počet stran výsledku

6

Strana od-do

126-131

Název nakladatele

AMER INST PHYSICS

Místo vydání

MELVILLE, NY 11747-4501 USA

Místo konání akce

Sozopol, BULGARIA

Datum konání akce

6. 12. 2012

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

312260000017