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# A new error estimate of the fast gauss transform

Baxter, B.J.C.B. and Roussos, George (2002) A new error estimate of the fast gauss transform. SIAM Journal on Scientific Computing 24 (1), pp. 257-259. ISSN 1064-8275.

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## Abstract

The fast Gauss transform of L. Greengard and J. Strain [SIAM J. Sci. Statist. Comput., 12 (1991), pp. 79--94] reduces the computational complexity of the evaluation of the sum of N Gaussians at M points in d-dimensional space from ${\cal O}(MN)$ to ${\cal O}(M+N)$ floating-point operations. In this note, we provide numerical evidence that the error estimate of Lemma 2.1 in [SIAM J. Sci. Statist. Comput., 12 (1991), pp. 79--94] is erroneous and then proceed to calculate a replacement error estimate for the fast Gauss transform, incorporating an improved upper bound for Hermite functions.

Item Type: Article School of Business, Economics & Informatics > Computer Science and Information Systems Sarah Hall 11 Oct 2021 17:15 11 Oct 2021 17:15 https://eprints.bbk.ac.uk/id/eprint/46268