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

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

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.