Journal
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Volume 19, Issue 1, Pages 17-48Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2005.01.003
Keywords
exponential sums; Hankel matrices; Prony's method; separated representations
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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.
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