Sparse approximation of functions using sums of exponentials and AAK theory

  • Authors:

  • Fredrik Andersson;Marcus Carlsson;Maarten V. de Hoop

  • Affiliations:

  • Centre for Mathematical Sciences, Lund University, Box 118, SE-22100, Lund, Sweden;Center for Computational and Applied Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA;Center for Computational and Applied Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907, USA

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2011

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Abstract

We consider the problem of approximating functions by sums of few exponentials functions, either on an interval or on the positive half-axis. We study both continuous and discrete cases, i.e. when the function is replaced by a number of equidistant samples. Recently, an algorithm has been constructed by Beylkin and Monzon for the discrete case. We provide a theoretical framework for understanding how this algorithm relates to the continuous case.