2 citations · 5 across the 12 of their papers we have counts for
5 papers · 1 filter
Conditioning of partial nonuniform Fourier matrices with clustered nodes
Dmitry Batenkov, Laurent Demanet, Gil Goldman +1
We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with arbitrary "off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the…
Geometry and Singularities of Prony varieties
Gil Goldman, Yehonatan Salman, Yosef Yomdin
We start a systematic study of the topology, geometry and singularities of the Prony varieties , defined by the first equations of the classical Prony system $$\sum_{…
On algebraic properties of low rank approximations of Prony systems
Gil Goldman, Yosef Yomdin
We consider the reconstruction of spike train signals of the form from their moments measurements $m_k(F)=\int x^k F(x) dx = \sum_{i=1}^d a_ix…
Prony Scenarios and Error Amplification in a Noisy Spike-Train Reconstruction
Gil Goldman, Yehonatan Salman, Yosef Yomdin
The paper is devoted to the characterization of the geometry of Prony curves arising from spike-train signals. We give a sufficient condition which guarantees the blowing up of the…
Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view
Gil Goldman, Yehonatan Salman, Yosef Yomdin
This is a survey paper discussing one specific (and classical) system of algebraic equations - the so called "Prony system". We provide a short overview of its unusually wide conne…