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SIAM J. on Numerical Analysis / Volume 30 / Issue 2

SIAM J. Numer. Anal. 30, pp. 507-537 (31 pages)

Using the Refinement Equation for Evaluating Integrals of Wavelets

Wolfgang Dahmen and Charles A. Micchelli

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The Wavelet Galerkin Method for solving partial differential equations leads to the problem of computing integrals of products of derivatives of wavelets. This paper studies the problem from the point of view of stationary subdivision schemes. One of the main results is to identify these integrals as components of the unique solution of a certain eigenvector-moment problem associated with the coefficients of the refinement equation. Asymptotic expansions for the corresponding subdivision schemes form an important ingredient of our approach.

© 1993 Society for Industrial and Applied Mathematics

KEYWORDS

AMS Subject Headings

65D20, 65R10, 39B40, 41A60

PUBLICATION DATA

ISSN:

0036-1429 (print)  
1095-7170 (online)

Publisher:

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received April 29, 1991
Accepted March 30, 1992
Permalink
http://dx.doi.org/10.1137/0730024

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