Wavelet basis of cubic splines on the hypercube satisfying
homogeneous boundary conditions

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Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions

Přehled o publikaci

J 2015

Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions

CERNA, Dana and Václav FINĚK

Basic information

Original name

Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions

Authors

CERNA, Dana (203 Czech Republic, guarantor, belonging to the institution) and Václav FINĚK (203 Czech Republic, belonging to the institution)

Edition

International Journal of Wavelets, Multiresolution and Information Processing, Singapore, World Scientific, 2015, 1793-690X

Other information

Language

English

Type of outcome

Article in a journal

Field of Study

General mathematics

Country of publisher

Singapore

Confidentiality degree

is not subject to a state or trade secret

References:

URL

RIV identification code

RIV/46747885:24510/15:#0001251

Organization

Faculty of Science, Humanities and Education – Technical University of Liberec – Repository

DOI

http://dx.doi.org/10.1142/S0219691315500149

UT WoS

000355330800002

Keywords in English

Construction; wavelet; cubic spline; homogeneous Dirichlet boundary conditions; condition number; elliptic problem; Galerkin method; conjugate gradient method

Changed: 1/4/2016 09:22, Dana Černá

Abstract

V originále

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.

Cite

CERNA, Dana and Václav FINĚK. Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions. International Journal of Wavelets, Multiresolution and Information Processing. Singapore: World Scientific, 2015, vol. 13, No 3, p. nestránkováno, 21 pp. ISSN 1793-690X. Available from: https://dx.doi.org/10.1142/S0219691315500149.

@article{20546,
   author = {Cerna, Dana and Finěk, Václav},
   article_location = {Singapore},
   article_number = {3},
   doi = {http://dx.doi.org/10.1142/S0219691315500149},
   keywords = {Construction; wavelet; cubic spline; homogeneous Dirichlet boundary conditions; condition number; elliptic problem; Galerkin method; conjugate gradient method},
   language = {eng},
   issn = {1793-690X},
   journal = {International Journal of Wavelets, Multiresolution and Information Processing},
   title = {Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions},
   url = {http://www.worldscientific.com/doi/abs/10.1142/S0219691315500149},
   volume = {13},
   year = {2015}
}

TY  - JOUR
ID  - 20546
AU  - Cerna, Dana - Finěk, Václav
PY  - 2015
TI  - Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions
JF  - International Journal of Wavelets, Multiresolution and Information Processing
VL  - 13
IS  - 3
SP  - nestránkováno
EP  - nestránkováno
PB  - World Scientific
SN  - 1793-690X
KW  - Construction
KW  - wavelet
KW  - cubic spline
KW  - homogeneous Dirichlet boundary conditions
KW  - condition number
KW  - elliptic problem
KW  - Galerkin method
KW  - conjugate gradient method
UR  - http://www.worldscientific.com/doi/abs/10.1142/S0219691315500149
L2  - http://www.worldscientific.com/doi/abs/10.1142/S0219691315500149
N2  - 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.
ER  -

CERNA, Dana and Václav FINĚK. Wavelet basis of cubic splines on the hypercube satisfying homogeneous boundary conditions. \textit{International Journal of Wavelets, Multiresolution and Information Processing}. Singapore: World Scientific, 2015, vol.~13, No~3, p.~nestránkováno, 21 pp. ISSN~1793-690X. Available from: https://dx.doi.org/10.1142/S0219691315500149.