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Fritz Keinert, Department of Mathematics, Iowa State University
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PostPosted: Tue Nov 03, 1992 4:49 pm    
Subject: paper available
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paper available

Author: Fritz Keinert
Dept. of Mathematics
Iowa State University
Ames, IA 50011
(515) 294-5223
keinert@iastate.edu

Title: Biorthogonal Wavelets for Fast Matrix Computations

Status: Submitted to "Applied and Computational Harmonic Analysis"
October 1992

Abstract: In (G. Beylkin, R. Coifman, V. Rokhlin, Fast wavelet
transforms and numerical algorithms: I, Comm. Pure Appl.
Math. 44(1991), 141--183), Beylkin et al. introduced a
wavelet-based algorithm that converts matrices of a certain
type into highly sparse matrices, as the basis for efficient
approximate calculations. Compression is achieved by doing
a wavelet decomposition of the matrix and setting small
entries to zero. The wavelets best suited for achieving the
highest possible compression with this algorithm are
Daubechies wavelets, while coiflets lead to a faster
decomposition algorithm at slightly lesser compression. We
demonstrate how the same algorithm can be based on
biorthogonal instead of orthogonal wavelets, and derive two
classes of biorthogonal wavelets that achieve high
compression and high decomposition speed, respectively. In
numerical experiments, these biorthogonal wavelets achieved
both higher compression and higher speed than their wavelet
counterparts, at comparable accuracy.

Availability: anonymous ftp from pollux.math.iastate.edu (129.186.52.4),
in directory pub/keinert. Get file README first.
- biortho.dvi (text of paper, without figures), 84K
- biortho_figures.ps (figures only, in PostScript), 925K
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