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Multiwavelet Representation of Functions and Operators
by
Chuan Li
The University of Tennessee, Knoxville
Multiwavelets is one of the newer "fast" methods of computational complexity O(NLogN). Adaptive solutions of a large class of integral equations to high precision can be achieved using multiwavelet bases. We present the construction of Alpert's multiwavelet basis, the fundamental idea of this fast algorithm, and its error estimate. The method can be extended to higher dimensions via tensor products. An example of the Hilbert transform in 1D and a solution to a Poisson equation in 2D using Alpert’s multiwavelet basis are also given in this talk.
Date received: August 30, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cauf-62.