The Construction of Well-Conditioned Wavelet Basis Based on Quadratic B-Splines

Kód výsledku v IS VaVaI

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Výsledek na webu

<a href="http://proceedings.aip.org" target="_blank" >http://proceedings.aip.org</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

The Construction of Well-Conditioned Wavelet Basis Based on Quadratic B-Splines

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. The essential steps are: to transform the variational formulation into the well-conditioned infinite-dimensional l2-problem, to find the convergent iteration process for this infinite-dimensional l2-problem and finally to derive its finite-dimensional approximation which works with an inexact right hand-side and an approximate matrix-vector multiplication. It should provide an approximation of the unknown solution up to a given target accuracy epsilon. To perform this scheme efficiently, it is necessary to have at one's disposal suitable wavelet bases which fit well into this concept. Wavelets should have short supports and vanishing moments, be smooth and known in closed form, and a corresponding wavelet basis should be well-conditioned. In our contribution, we propose a quadratic wavelet basis adapted to the interval [0,1] which pres

Název v anglickém jazyce

The Construction of Well-Conditioned Wavelet Basis Based on Quadratic B-Splines

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. The essential steps are: to transform the variational formulation into the well-conditioned infinite-dimensional l2-problem, to find the convergent iteration process for this infinite-dimensional l2-problem and finally to derive its finite-dimensional approximation which works with an inexact right hand-side and an approximate matrix-vector multiplication. It should provide an approximation of the unknown solution up to a given target accuracy epsilon. To perform this scheme efficiently, it is necessary to have at one's disposal suitable wavelet bases which fit well into this concept. Wavelets should have short supports and vanishing moments, be smooth and known in closed form, and a corresponding wavelet basis should be well-conditioned. In our contribution, we propose a quadratic wavelet basis adapted to the interval [0,1] which pres

Druh

D - Stať ve sborníku

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 statě ve sborníku

AIP Conference Proceedings

ISBN

9780735410916

ISSN

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e-ISSN

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Počet stran výsledku

4

Strana od-do

230-233

Název nakladatele

American Institute of Physics

Místo vydání

New York

Místo konání akce

Kos, Greece

Datum konání akce

1. 1. 2012

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

310698100055