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 a Václav FINĚK

Základní údaje

Originální název

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

Autoři

CERNA, Dana (203 Česká republika, garant, domácí) a Václav FINĚK (203 Česká republika, domácí)

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

Obecná matematika

Stát vydavatele

Singapur

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Kód RIV

RIV/46747885:24510/15:#0001251

Organizace

Fakulta přírodovědně-humanitní a pedagogická – Technická univerzita v Liberci – Repozitář

DOI

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

UT WoS

000355330800002

Klíčová slova anglicky

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

Změněno: 1. 4. 2016 09:22, Dana Černá

Anotace

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.

Citovat

CERNA, Dana a 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, roč. 13, č. 3, s. nestránkováno, 21 s. ISSN 1793-690X. Dostupné z: 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 a 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, roč.~13, č.~3, s.~nestránkováno, 21 s. ISSN~1793-690X. Dostupné z: https://dx.doi.org/10.1142/S0219691315500149.