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Nonlinear approximation of functions in two dimensions by sums of exponential functions

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Author

Summary, in English

We consider the problem of approximating a given function in two dimensions by a sum of exponential functions, with complex-valued exponents and coefficients. In contrast to Fourier representations where the exponentials are fixed, we consider the nonlinear problem of choosing both the exponents and coefficients. In this way we obtain accurate approximations with only few terms. Our approach is built on recent work done by G. Beylkin and L Monzon in the one-dimensional case. We provide constructive methods for how to find the exponents and the coefficients, and provide error estimates. We also provide numerical simulations where the method produces sparse approximations with substantially fewer terms than what a Fourier representation produces for the same accuracy. (c) 2009 Elsevier Inc. All rights reserved.

Publishing year

2010

Language

English

Pages

156-181

Publication/Series

Applied and Computational Harmonic Analysis

Volume

29

Issue

2

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • Sparse representations
  • Systems of polynomial equations
  • Frequency estimation
  • Nonlinear approximation
  • Prony's method in
  • several variables
  • Hankel operators
  • AAK theory in several variables

Status

Published

Research group

  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 1096-603X