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Fast Gauss transform

This is a special case of the fast summation method, we compute approximations of the following sums. Given complex coefficients $ \alpha_k \in \ensuremath{\mathbb{C}}$ and source nodes $ x_k\in[-\frac{1}{4},\frac{1}{4}]$ , our goal consists in the fast evaluation of the sum

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

at the target nodes $ y_j \in [-\frac{1}{4},\frac{1}{4}]$ , $ j=1,\ldots,M$ , where $ \sigma =a +{\rm i} b$ , $ a>0$ , $ b\in\ensuremath{\mathbb{R}}$ , denotes a complex parameter. For details see [37] and the related paper [2] for applications. All numerical examples of [37] are produced by the programs in applications/fastgauss.



Jens Keiner 2006-11-20