On approximation of functions by exponential sums

被引：230
作者：
Beylkin, G [1 ]
Monzón, L [1 ]
机构：
[1] Univ Colorado, Dept Appl Math, Boulder, CO 80309 USA
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2005年 / 19卷 / 01期
基金：
美国国家科学基金会;
关键词：
exponential sums; Hankel matrices; Prony's method; separated representations;
D O I：
10.1016/j.acha.2005.01.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a new approach, and associated algorithms, for the efficient approximation of functions and sequences by short linear combinations of exponential functions with complex-valued exponents and coefficients. These approximations are obtained for a finite but arbitrary accuracy and typically have significantly fewer terms than Fourier representations. We present several examples of these approximations and discuss applications to fast algorithms. In particular, we show how to obtain a short separated representation (sum of products of one-dimensional functions) of certain multi-dimensional Green's functions. (c) 2005 Elsevier Inc. All rights reserved.
引用
收藏
页码：17 / 48
页数：32
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