Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions
Result description
In this paper, we propose a construction of a new cubic spline-wavelet basis on the hypercube satisfying homogeneous Dirichlet boundary conditions. Wavelets have two vanishing moments. Stiffness matrices arising from discretization of elliptic problems using a constructed wavelet basis have uniformly bounded condition numbers and we show that these condition numbers are small. We present quantitative properties of the constructed basis and we provide a numerical example to show the efficiency of the Galerkin method using the constructed basis.
Keywords
Constructionwaveletcubic splinehomogeneous Dirichlet boundary conditionscondition numberelliptic problemGalerkin methodconjugate gradient method
The result's identifiers
Result code in IS VaVaI
Result on the web
http://www.worldscientific.com/doi/abs/10.1142/S0219691315500149
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions
Original language description
In this paper, we propose a construction of a new cubic spline-wavelet basis on the hypercube satisfying homogeneous Dirichlet boundary conditions. Wavelets have two vanishing moments. Stiffness matrices arising from discretization of elliptic problems using a constructed wavelet basis have uniformly bounded condition numbers and we show that these condition numbers are small. We present quantitative properties of the constructed basis and we provide a numerical example to show the efficiency of the Galerkin method using the constructed basis.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Wavelets, Multiresolution and Information Processing
ISSN
1793-690X
e-ISSN
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Volume of the periodical
13
Issue of the periodical within the volume
3
Country of publishing house
SG - SINGAPORE
Number of pages
21
Pages from-to
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UT code for WoS article
000355330800002
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2015