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Numerical computation of multidimensional Fourier integrals
Author

Gordon Inverarity
Organization: Met Office, U.K.
Old MathSource #

0212-128
Revision date

2002-07-01
Description

The NFourierIntegral package adaptively computes multidimensional Fourier integrals over finite integration ranges. Each integral is evaluated over sets of equally-spaced values in each dimension whose Cartesian product spans an arbitrary region of transform variable space. With suitable truncation, the package can be used to approximate multidimensional Fourier transforms. The underlying algorithm is that of Inverarity (2002), which generalizes the one-dimensional algorithm of Bailey and Swarztrauber (1994). For a given number of function evaluations, the multidimensional midpoint rule is used to approximate the integral as a multidimensional circular convolution, which is then evaluated using fast Fourier transforms. It is implemented adaptively using Richardson extrapolation, also known as extrapolation to the limit.

References:

Bailey, D.H. and Swartrauber, P.N., "A fast method for the numerical evaluation of continuous Fourier and Laplace transforms", SIAM J. Sci. Comput., 15, 1105-1110 (1994)

Inverarity, G.W., "Fast computation of multidimensional Fourier integrals", SIAM J. Sci. Comput., 24, 645-651 (2002) (http://epubs.siam.org/sam-bin/dbq/article/38647)

(c) British Crown Copyright 2002
Subject

*Mathematics > Calculus and Analysis
Keywords

Fourier, Fourier transform, Fourier integral, multi-dimensional, numerical integration
Downloads

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INSTALL.txt (1.1 KB) - Text file
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Calculus.sit (17.3 KB) - Macintosh Stuffit archive
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Calculus.tar.gz (16.5 KB) - GZIP archive
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Calculus.zip (18.7 KB) - ZIP archive