Quadratic Spline Wavelets with Short Support Satisfying Homogeneous Boundary Conditions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F18%3A00005664" target="_blank" >RIV/46747885:24510/18:00005664 - isvavai.cz</a>
Result on the web
<a href="http://etna.mcs.kent.edu/volumes/2011-2020/vol48/abstract.php?vol=48&pages=15-39" target="_blank" >http://etna.mcs.kent.edu/volumes/2011-2020/vol48/abstract.php?vol=48&pages=15-39</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1553/etna_vol48s15" target="_blank" >10.1553/etna_vol48s15</a>
Alternative languages
Result language
angličtina
Original language name
Quadratic Spline Wavelets with Short Support Satisfying Homogeneous Boundary Conditions
Original language description
In this paper, we construct a new quadratic spline-wavelet basis on the interval and on the unit square satisfying homogeneous Dirichlet boundary conditions of the first order. The wavelets have one vanishing moment and the shortest support among quadratic spline wavelets with at least one vanishing moment adapted to the same type of boundary conditions. The stiffness matrices arising from the discretization of the second-order elliptic problems using the constructed wavelet basis have uniformly bounded condition numbers, and the condition numbers are small. We present some quantitative properties of the constructed basis. We provide numerical examples to show that the Galerkin method and the adaptive wavelet method using our wavelet basis require fewer iterations than methods with other quadratic spline wavelet bases. Moreover, due to the small support of the wavelets, when using these methods with the new wavelet basis, the system matrix is sparser, and thus one iteration requires a smaller number of floating point operations than for other quadratic spline wavelet bases.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS
ISSN
1068-9613
e-ISSN
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Volume of the periodical
48
Issue of the periodical within the volume
neuvedeno
Country of publishing house
US - UNITED STATES
Number of pages
25
Pages from-to
15-39
UT code for WoS article
000459295400002
EID of the result in the Scopus database
2-s2.0-85045282491