A new error estimate of the fast Gauss transform

被引：20

作者：

Baxter, BJC ^{[1
]}

Roussos, G ^{[1
]}

机构：

[1] Univ London Imperial Coll Sci & Technol, Dept Math, London SW7 2BZ, England

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2002年 / 24卷 / 01期

关键词：

fast Gauss transform; fast algorithms;

D O I：

10.1137/S1064827501396920

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 O(MN) to 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.

引用

页码：257 / 259

页数：3