Wavelets of Hermite cubic splines on the interval

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F12%3A%230000826" target="_blank" >RIV/46747885:24510/12:#0000826 - isvavai.cz</a>

Výsledek na webu

<a href="http://proceedings.aip.org/resource/2/apcpcs/1497/1/138_1?isAuthorized=no" target="_blank" >http://proceedings.aip.org/resource/2/apcpcs/1497/1/138_1?isAuthorized=no</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/1.4766778" target="_blank" >10.1063/1.4766778</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Wavelets of Hermite cubic splines on the interval

Popis výsledku v původním jazyce

In 2000, W. Dahmen et al. proposed a construction of biorthogonal multi-wavelets adapted to the interval [0,1] on the basis of Hermite cubic splines. They started with Hermite cubic splines as the primal scaling bases on R. Then, they constructed dual scaling bases on R consisting of continuous functions with small supports and with polynomial exactness of order 2. Consequently, they derived primal and dual boundary scaling functions retaining the polynomial exactness. This ensures vanishing moments ofthe corresponding wavelets. Finally, they applied the method of stable completions to construct the corresponding primal and dual multi-wavelets on the interval. In recent years, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. In this contribution, we shortly review these constructions, use these wavelets to solve numerically differential equations, and compare their performance with a hierarchical basis in finite element methods.

Název v anglickém jazyce

Wavelets of Hermite cubic splines on the interval

Popis výsledku anglicky

In 2000, W. Dahmen et al. proposed a construction of biorthogonal multi-wavelets adapted to the interval [0,1] on the basis of Hermite cubic splines. They started with Hermite cubic splines as the primal scaling bases on R. Then, they constructed dual scaling bases on R consisting of continuous functions with small supports and with polynomial exactness of order 2. Consequently, they derived primal and dual boundary scaling functions retaining the polynomial exactness. This ensures vanishing moments ofthe corresponding wavelets. Finally, they applied the method of stable completions to construct the corresponding primal and dual multi-wavelets on the interval. In recent years, several more simple constructions of wavelet bases based on Hermite cubic splines were proposed. In this contribution, we shortly review these constructions, use these wavelets to solve numerically differential equations, and compare their performance with a hierarchical basis in finite element methods.

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

138-143

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

312260000019