Approximating the Gaussian as a Sum of Exponentials and its Applications to the Fast Gauss Transform  

作　　者：Shidong Jiang Leslie Greengard 

机构地区：[1]Department of Mathematical Sciences,New Jersey Institute of Technology,Newark,NJ 07102,USA [2]Courant Institute of Mathematical Sciences,New York University,New York,NY 10012,USA [3]Center for Computational Mathematics,Flatiron Institute,Simons Foundation,New York,NY 10010,USA

出　　处：《Communications in Computational Physics》2022年第1期1-26,共26页计算物理通讯（英文）

基　　金：S.Jiang was supported in part by the United States National Science Foundation under grant DMS-1720405.

摘　　要：We develop efficient and accurate sum-of-exponential(SOE)approximations for the Gaussian using rational approximation of the exponential function on the negative real axis.Six digit accuracy can be obtained with eight terms and ten digit accuracy can be obtained with twelve terms.This representation is of potential interest in approximation theory but we focus here on its use in accelerating the fast Gauss transform(FGT)in one and two dimensions.The one-dimensional scheme is particularly straightforward and easy to implement,requiring only twenty-four lines of MATLAB code.The two-dimensional version requires some care with data structures,but is significantly more efficient than existing FGTs.Following a detailed presentation of the theoretical foundations,we demonstrate the performance of the fast transforms with several numerical experiments.

关 键 词：Fast Gauss transform sum-of-exponential approximation best rational approximation model reduction 

分 类 号：O17[理学—数学]