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Statements

Subject Item
n2:RIV%2F46747885%3A24510%2F12%3A%230000825%21RIV13-MSM-24510___
rdf:type
n8:Vysledek skos:Concept
rdfs:seeAlso
http://proceedings.aip.org/resource/2/apcpcs/1497/1/126_1?isAuthorized=no
dcterms:description
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 scaling functions 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 wavelet methods and non-adaptive sparse grid methods. Furthermore, we even improve the condition numbers of the stiffness matrices by including lower levels. 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 scaling functions 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 wavelet methods and non-adaptive sparse grid methods. Furthermore, we even improve the condition numbers of the stiffness matrices by including lower levels.
dcterms:title
Wavelet Bases on the Interval with Short Support and Vanishing Moments Wavelet Bases on the Interval with Short Support and Vanishing Moments
skos:prefLabel
Wavelet Bases on the Interval with Short Support and Vanishing Moments Wavelet Bases on the Interval with Short Support and Vanishing Moments
skos:notation
RIV/46747885:24510/12:#0000825!RIV13-MSM-24510___
n8:predkladatel
n11:orjk%3A24510
n3:aktivita
n19:S
n3:aktivity
S
n3:dodaniDat
n6:2013
n3:domaciTvurceVysledku
n12:1173782 n12:3694674 n12:2764261
n3:druhVysledku
n23:D
n3:duvernostUdaju
n16:S
n3:entitaPredkladatele
n17:predkladatel
n3:idSjednocenehoVysledku
180753
n3:idVysledku
RIV/46747885:24510/12:#0000825
n3:jazykVysledku
n22:eng
n3:klicovaSlova
cubic spline; wavelet; construction; condition number; biharmonic equation
n3:klicoveSlovo
n5:condition%20number n5:construction n5:biharmonic%20equation n5:cubic%20spline n5:wavelet
n3:kontrolniKodProRIV
[820EA5AF22B7]
n3:mistoKonaniAkce
Sozopol, BULGARIA
n3:mistoVydani
MELVILLE, NY 11747-4501 USA
n3:nazevZdroje
APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12)
n3:obor
n18:BA
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
3
n3:rokUplatneniVysledku
n6:2012
n3:tvurceVysledku
Bímová, Daniela Finěk, Václav Černá, Dana
n3:typAkce
n20:EUR
n3:wos
312260000017
n3:zahajeniAkce
2012-12-06+01:00
s:numberOfPages
6
n13:doi
10.1063/1.4766776
n10:hasPublisher
AMER INST PHYSICS
n21:isbn
978-0-7354-1111-1
n15:organizacniJednotka
24510