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Fast Gauss transforms with complex parameters using NFFT

Fast Gauss transforms with complex parameters using NFFT

This library of C functions computes approximations of sums of the following form. Given complex coefficients $ \alpha_k \in \mathbb{C}$ and source knots $ x_k\in[-\frac{1}{4},\frac{1}{4}]$, our goal consists in the fast evaluation of the sum

$\displaystyle f(y)=\sum_{k=1}^N \alpha_k \rm {e}^{-\sigma\vert y-x_k\vert^2}$

at the target knots $ y_j \in [-\frac{1}{4},\frac{1}{4}]$, $ j=1,\ldots,M$, where $ \sigma = a + {\rm i} b$, $ a>0,b\in \mathbb{R}$ denotes a complex parameter.


The algorithms are implemented by Stefan Kunis in ./applications/fastgauss. Related paper are

oKunis, S., Potts, D. and Steidl, G.
Fast Gauss transforms with complex parameters using NFFTs.
J. Numer. Math. 14, 295-303.   (full paper ps, pdf),   2006