Gil Goldman

activity

20172021

most citedSingle-exponential bounds for the smallest singular value of Vandermonde matrices in the sub-Rayleigh regime

2 citations · 3 across the 2 of their papers we have counts for

collaborators

8 papers

math.NA2021★ 2 cited

Single-exponential bounds for the smallest singular value of Vandermonde matrices in the sub-Rayleigh regime

Dmitry Batenkov, Gil Goldman

Following recent interest by the community, the scaling of the minimal singular value of a Vandermonde matrix with nodes forming clusters on the length scale of Rayleigh distance o…

math.CA2019

Exponential Taylor domination

Omer Friedland, Gil Goldman, Yosef Yomdin

Let $f (z) = \sum_{k = 0}^{\infty} a_{k} z^{k}$ be an analytic function in a disk $D_{R}$ of radius $R > 0$ , and assume that $f$ is $p$ -valent in $D_{R}$ , i.e. it takes each value $c\in{\mathbb C…

math.NA2019

The spectral properties of Vandermonde matrices with clustered nodes

Dmitry Batenkov, Benedikt Diederichs, Gil Goldman +1

We study rectangular Vandermonde matrices $V$ with $N + 1$ rows and $s$ irregularly spaced nodes on the unit circle, in cases where some of the nodes are "clustered" togethe…

math.NA2019

Super-resolution of near-colliding point sources

Dmitry Batenkov, Gil Goldman, Yosef Yomdin

We consider the problem of stable recovery of sparse signals of the form $F (x) = j = 1 \sum d a_{j} δ (x - x_{j}), x_{j} \in R, a_{j} \in C,$ from their spectral measureme…

math.NA2018

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…

math.CA2018

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 $F (x) = i = 1 \sum d a_{i} δ (x - x_{i}),$ from their moments measurements $m_k(F)=\int x^k F(x) dx = \sum_{i=1}^d a_ix…