Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast solution View Full Text


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Article Info

DATE

1993-10

AUTHORS

W. Dahmen, S. Prössdorf, R. Schneider

ABSTRACT

This is the second part of two papers which are concerned with generalized Petrov-Galerkin schemes for elliptic periodic pseudodifferential equations in ℝn. This setting covers classical Galerkin methods, collocation, and quasi-interpolation. The numerical methods are based on a general framework of multiresolution analysis, i.e. of sequences of nested spaces which are generated by refinable functions. In this part, we analyse compression techniques for the resulting stiffness matrices relative to wavelet-type bases. We will show that, although these stiffness matrices are generally not sparse, the order of the overall computational work which is needed to realize a certain accuracy is of the formO(N(logN)b), whereN is the number of unknowns andb ≥ 0 is some real number. More... »

PAGES

259-335

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02072014

DOI

http://dx.doi.org/10.1007/bf02072014

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1018913200


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