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Wavelet Methods for Elliptic Partial Differential Equations$
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Karsten Urban

Print publication date: 2008

Print ISBN-13: 9780198526056

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780198526056.001.0001

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Adaptive Wavelet Methods

Adaptive Wavelet Methods

Chapter:
(p.186) 7 Adaptive Wavelet Methods
Source:
Wavelet Methods for Elliptic Partial Differential Equations
Author(s):

Karsten Urban

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198526056.003.0007

This chapter starts by adaptively approximating a given function and introduce the main theoretical concepts. After describing the more classical approach to adaptivity based upon a-posteriori error estimates, it shows the somewhat different perspective of adaptive wavelet methods. Given an operator equation, an equivalent infinite-dimensional problem on sequence spaces is introduced. In order to obtain a computable method, the infinite operator is replaced by an approximate application. The resulting schemes are described, analyzed and compared by numerical experiments. An outlook to nonlinear operators is given.

Keywords:   best N-term approximation, adaptive wavelet methods, compressible matrices, asymptotical optimal, nonlinear functions, Besov spaces

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