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 …

We derive a new generalization of Prony's method to reconstruct M-sparse expansions of
(generalized) eigenfunctions of linear operators from only $\mathcal {O}(M) $ suitable values …

In data analysis and signal processing, the recovery of structured functions from the given
sampling values is a fundamental problem. Many methods generalized from the Prony …

The generalized Prony method is a reconstruction technique for a large variety of sparse
signal models that can be represented as sparse expansions into eigenfunctions of a linear …

We present a dimension-incremental algorithm for the nonlinear approximation of high-
dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to …

We study the problem of reconstructing a sparse polynomial in a basis of Chebyshev
polynomials (Chebyshev basis in short) from given samples on a Chebyshev grid of [− 1, 1] …

We present Hermite polynomial interpolation algorithms that for a sparse univariate
polynomial f with coefficients from a field compute the polynomial from fewer points than the …

Signal sparsity plays an essential role in signal compression and reconstruction. Prony-like
methods are widely used in the relevant applications eg, the recovery of signals with finite …

In this paper, we propose a general strategy for rapidly computing sparse Legendre
expansions. The resulting methods yield a new class of fast algorithms capable of …

Sparse polynomial interpolation with Bernstein polynomials Page 1 Turkish Journal of
Mathematics Volume 45 Number 5 Article 15 1-1-2021 Sparse polynomial interpolation with …