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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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Multiscale Approximation and Multiresolution

Multiscale Approximation and Multiresolution

Chapter:
(p.9) 2 Multiscale Approximation and Multiresolution
Source:
Wavelet Methods for Elliptic Partial Differential Equations
Author(s):

Karsten Urban

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198526056.003.0002

This chapter considers a piecewise constant approximation of a given function and introduces the Haar system for that purpose. This is compared with a piecewise linear approximation, highlighting differences and similar properties. Based upon this, the notion of multiresolution is introduced. Several examples of generating scaling functions are given.

Keywords:   Haar function, hat function, multiresolution analysis, refinable function, Daubechies' function, B-splines, cascade algorithm

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