Details
| Original language | English |
|---|---|
| Pages (from-to) | 131-149 |
| Number of pages | 19 |
| Journal | Mathematische Nachrichten |
| Volume | 244 |
| Publication status | Published - 2002 |
| Externally published | Yes |
Abstract
In L2((0, 1)2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.
Keywords
- Anisotropic Besov spaces, Dominating mixed smoothness, Hyperbolic bases, N-term approximation, Tresholding, Wavelets
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Mathematische Nachrichten, Vol. 244, 2002, p. 131-149.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - N-term approximation in anisotropic function spaces
AU - Hochmuth, Reinhard
PY - 2002
Y1 - 2002
N2 - In L2((0, 1)2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.
AB - In L2((0, 1)2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one-dimensional biorthogonal wavelet bases on the interval (0, 1). Most well-known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases.
KW - Anisotropic Besov spaces
KW - Dominating mixed smoothness
KW - Hyperbolic bases
KW - N-term approximation
KW - Tresholding
KW - Wavelets
UR - http://www.scopus.com/inward/record.url?scp=0036402389&partnerID=8YFLogxK
U2 - 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G
DO - 10.1002/1522-2616(200210)244:1<131::AID-MANA131>3.0.CO;2-G
M3 - Article
AN - SCOPUS:0036402389
VL - 244
SP - 131
EP - 149
JO - Mathematische Nachrichten
JF - Mathematische Nachrichten
SN - 0025-584X
ER -