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We present a fast Gauss transform in one dimension using nearly optimalsum-of-exponentials approximations of the Gaussian kernel. For up to aboutten-digit accuracy, the approximations are obtained via best rationalapproximations of the exponential function on the negative real axis. Ascompared with existing fast Gauss transforms, the algorithm is straightforwardfor parallelization and very simple to implement, with only twenty-four linesof code in MATLAB. The most expensive part of the algorithm is on theevaluation of complex exponentials, leading to three to six complexexponentials FLOPs per point depending on the desired precision. Theperformance of the algorithm is illustrated via several numerical examples.

A fast Gauss transform in one dimension using sum-of-exponentials approximations