On Wavelet Matrix Compression for Differential Equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F11%3A%230000792" target="_blank" >RIV/46747885:24510/11:#0000792 - isvavai.cz</a>
Result on the web
<a href="http://proceedings.aip.org/resource/2/apcpcs/1389/1/1574_1?isAuthorized=no" target="_blank" >http://proceedings.aip.org/resource/2/apcpcs/1389/1/1574_1?isAuthorized=no</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.3637931" target="_blank" >10.1063/1.3637931</a>
Alternative languages
Result language
angličtina
Original language name
On Wavelet Matrix Compression for Differential Equations
Original language description
The design of most adaptive wavelet methods for solving differential equations follows a general concept proposed by A. Cohen, W. Dahmen and R. DeVore in [5, 6]. The essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l2 problem, finding of the convergent iteration process for the l2 problem and finally derivation of its finite dimensional version which works with an inexact right hand side and approximate matrix-vector multiplication. In ourcontribution, we shortly review all these parts with emphasis on the approximate matrix-vector multiplication. Efficient approximation of matrix-vector multiplication is enabled by an off-diagonal decay of entries of the wavelet stiffness matrix and bydecay of entries of load vector in wavelet coordinates. Besides an usual truncation in scale, we apply here also a truncation in space to compress wavelet stiffness matrices efficiently. At the end, we show some numerical experiments.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GP201%2F09%2FP641" target="_blank" >GP201/09/P641: Wavelet adaptive methods with stable bases</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011
ISBN
978-0-7354-0956-9
ISSN
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e-ISSN
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Number of pages
4
Pages from-to
1574-1577
Publisher name
American Institute of Physics
Place of publication
Melville, New York
Event location
Halkidiki, (Greece)
Event date
Jan 1, 2011
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
302239800378