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\iteman{io-port 05987091}
\itemau{Peter, Thomas; Potts, Daniel; Tasche, Manfred}
\itemti{Nonlinear approximation by sums of exponentials and translates.}
\itemso{SIAM J. Sci. Comput. 33, No. 4, 1920-1947 (2011).}
\itemab
The numerical solutions of two nonlinear approximation problems, motivated from engineering applications, are discussed. The first problem is determining all frequencies and coefficients involved in a finite linear sum of exponentials $h$ when finitely many perturbed uniform samples of $h$ are given. This problem is solved via the approximate Prony method and the stability of the solution in the square and uniform norm is confirmed.  The second problem is determining all shift parameters and coefficients in a linear combination of translates of a 1-periodic window function when finitely many perturbed uniform samples of it are given. This problem is reduced to the first one, applying the Fourier transform. Thus, its solution is stable in the square and uniform norm.  The advanced performance of the proposed algorithms is demonstrated by numerical experiments in the last section.
\itemrv{Roza Aceska (Skopje)}
\itemcc{}
\itemut{nonlinear approximation; exponential sum; exponential fitting; harmonic retrieval; sum of translates; approximate Prony method; nonuniform sampling; parameter estimation; least squares method; signal processing; signal recovery; singular value decomposition; matrix perturbation theory; perturbed rectangular Hankel matrix; stability; periodic window function; Fourier transform; numerical experiments}
\itemli{doi:10.1137/100790094}
\end