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MiS Preprint
102/2006

Fast and Exact Projected Convolution for Non-equidistant Grids - Extended Version

Wolfgang Hackbusch

Abstract

Usually, the fast evaluation of a convolution integral $\int_{\mathbb{R}}f(y)g(x-y)\mathrm{d}y$ requires that the functions $f,g$ are discretised on an equidistant grid in order to apply the fast Fourier transform. Here we discuss the efficient performance of the convolution in locally refined grids. More precisely, the convolution result is projected into some given locally refined grid. Under certain conditions, the overall costs are still $\mathcal{O}(N\log N),$ where $N$ is the sum of the dimensions of the subspaces containing $f$, $g$ and the resulting function.

Received:
Sep 25, 2006
Published:
Sep 25, 2006
MSC Codes:
44A35, 42A55
Keywords:
convolution integral, non-uniform grids, discrete convolution

Related publications

inJournal
2007 Repository Open Access
Wolfgang Hackbusch

Fast and exact projected convolution for non-equidistant grids

In: Computing, 80 (2007) 2, pp. 137-168