Wavelets on the Interval and Fast Wavelet Transforms

Vector-parallel Fast Wavelet Transforms

Parallel 2D fast (tensor) wavelet transform algorithms have been implemented using the transpose-split idea. They run successfully on the Fujitsu VPP 300 and will form part of the Scientiic Software Library of the VP and the VPP series. An alternative strategy based on parallelisation of 1D transforms yielding longer vector lengths is proposed and the merits of these approaches are compared. Fi...

Fast Wavelet Transforms and Numerical Algorithms

The purpose of this paper is to introduce a class of numerical algorithms designed for rapid application of dense matrices (or integral operators) to vectors. As is well-known, applying directly a dense N×N− matrix to a vector requires roughly N operations, and this simple fact is a cause of serious difficulties encountered in large-scale computations. For example, the main reason for the limit...

Parallel Performance of Fast Wavelet Transforms

We present a parallel 2D wavelet transform algorithm with modest communication requirements. Data are transmitted between nearest neighbors only and the amount is independent of the problem size as well as the number of processors. An analysis of the theoretical performance shows that the algorithm is scalable approaching perfect speedup as the problem size is increased. This performance is rea...

Parallel Implementation of Fast Wavelet Transforms

Orthogonal Wavelets on the Interval

In this paper we generalize the constructions 5], 8] and 21] of wavelets on the interval. These schemes give boundary modiications of compactly supported orthogonal wavelets 2 L 2 (R) with supp = ?N + 1; N], where N denotes the number of vanishing moments of. Our new scheme overcomes this restrictive condition. Furthermore, the constructions 5], 8], 21] involve Gram matrices for explicit orthog...