Prony methods for recovery of structured functions
Gerlind Plonka, Manfred Tasche · GAMM-Mitteilungen · 2014
Abstract In this survey, we describe the classical Prony method and whose relatives. We sketch a frequently used Prony–like method for equispaced sampled data, namely the ESPRIT method. The case of nonequispaced sampled data is discussed too. For the reconstruction of a sparse eigenfunction expansion, a generalized Prony method is presented. The Prony methods are applied to the recovery of structured functions (such as exponential sums and extended exponential sums) and of sparse vectors. The recovery of spline functions with arbitrary knots from Fourier data is also based on Prony methods. Finally, some numerical examples are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)