Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9500283 | Applied and Computational Harmonic Analysis | 2005 | 32 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Gregory Beylkin, Lucas MonzĂłn,