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

Fredrik Andersson, Marcus Carlsson, Maarten V. de Hoop

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17 Citations (SciVal)

Abstract

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.
Original languageEnglish
Pages (from-to)156-181
JournalApplied and Computational Harmonic Analysis
Volume29
Issue number2
DOIs
Publication statusPublished - 2010

Subject classification (UKÄ)

  • 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

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