About: Wavelet Bases on the Interval with Short Support and Vanishing Moments

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://proceedings.aip.org/resource/2/apcpcs/1497/1/126_1?isAuthorized=no
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. (en)
Title	Wavelet Bases on the Interval with Short Support and Vanishing Moments Wavelet Bases on the Interval with Short Support and Vanishing Moments (en)
skos:prefLabel	Wavelet Bases on the Interval with Short Support and Vanishing Moments Wavelet Bases on the Interval with Short Support and Vanishing Moments (en)
skos:notation	RIV/46747885:24510/12:#0000825!RIV13-MSM-24510___
http://linked.open...avai/riv/aktivita	S
http://linked.open...avai/riv/aktivity	S
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Černá, Dana Finěk, Václav Bímová, Daniela
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Technická univerzita v Liberci / Fakulta přírodovědně-humanitní a pedagogická
http://linked.open...dnocenehoVysledku	180753
http://linked.open...ai/riv/idVysledku	RIV/46747885:24510/12:#0000825
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	cubic spline; wavelet; construction; condition number; biharmonic equation (en)
http://linked.open.../riv/klicoveSlovo	wavelet condition number construction biharmonic equation cubic spline
http://linked.open...ontrolniKodProRIV	[820EA5AF22B7]
http://linked.open...v/mistoKonaniAkce	Sozopol, BULGARIA
http://linked.open...i/riv/mistoVydani	MELVILLE, NY 11747-4501 USA
http://linked.open...i/riv/nazevZdroje	APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12)
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	3 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...UplatneniVysledku	2012
http://linked.open...iv/tvurceVysledku	Finěk, Václav Černá, Dana Bímová, Daniela
http://linked.open...vavai/riv/typAkce	EUR - Evropská
http://linked.open...ain/vavai/riv/wos	312260000017
http://linked.open.../riv/zahajeniAkce	2012-12-06 (xsd:date)
number of pages	6 (xsd:int)
http://bibframe.org/vocab/doi	10.1063/1.4766776
http://purl.org/ne...btex#hasPublisher	AMER INST PHYSICS
https://schema.org/isbn	978-0-7354-1111-1
http://localhost/t...ganizacniJednotka	24510

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