Rapid evaluation of radial basis functions
Journal of Computational and Applied Mathematics
A sharp error estimate for the fast Gauss transform
Journal of Computational Physics
Entropy Minimization for Shadow Removal
International Journal of Computer Vision
The uselessness of the Fast Gauss Transform for summing Gaussian radial basis function series
Journal of Computational Physics
Rapid evaluation of radial basis functions
Journal of Computational and Applied Mathematics
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
An efficient and easily parallelizable algorithm for pricing weather derivatives
LSSC'05 Proceedings of the 5th international conference on Large-Scale Scientific Computing
Fast Approximation of the Discrete Gauss Transform in Higher Dimensions
Journal of Scientific Computing
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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.