Gil Goldman

activity

20162024

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

2 citations · 5 across the 12 of their papers we have counts for

collaborators

16 papers

math.CA2024

Lower bounds for high derivatives of smooth functions with given zeros

Gil Goldman, Yosef Yomdin

Let $f : B^{n} \to R$ be a $d + 1$ times continuously differentiable function on the unit ball $B^{n}$ , with $max_{z \in B^{n}} ∣ f (z) ∣ = 1$ . A well-known fact is that if $f$ …

math.CA2023

Higher derivatives of functions with zeros on algebraic curves

Gil Goldman, Yosef Yomdin

Let $f : B^{n} \to R$ be a $d + 1$ times continuously differentiable function on the unit ball $B^{n}$ , with $max_{z \in B^{n}} ∥ f (z) ∥ = 1$ . A well-known fact is that if…

math.CA2023

higher derivatives of functions with given critical points and values

Gil Goldman, Yosef Yomdin

Let $f : B^{n} \to R$ be a $d + 1$ times continuously differentiable function on the unit ball $B^{n}$ , with $max_{z \in B^{n}} ∥ f (z) ∥ = 1$ . A well-known fact is that if $…

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.NA2018

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 $S_{q} (μ)$ , defined by the first $q + 1$ equations of the classical Prony system $$\sum_{…

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…

eess.SP2018★ 2 cited

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…

math.NA2018

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…

math.CA2017★ 1 cited

Algebraic Geometry of Error Amplification: the Prony leaves

Dmitry Batenkov, Gil Goldman, Yehonatan Salman +1

We provide an overview of some results on the "geometry of error amplification" in solving Prony system, in situations where the nodes near-collide. It turns out to be governed by…

math.CA2017

Accuracy of reconstruction of spike-trains with two near-colliding nodes

Andrey Akinshin, Gil Goldman, Vladimir Golubyatnikov +1

We consider a signal reconstruction problem for signals $F$ of the form $F (x) = \sum_{j = 1}^{d} a_{j} δ (x - x_{j}),$ from their moments $m_{k} (F) = \int x^{k} F (x) d x .$ We assume $m_k…

math.CA2017

Geometry of error amplification in solving Prony system with near-colliding nodes

Andrey Akinshin, Gil Goldman, Yosef Yomdin

We consider a reconstruction problem for ``spike-train'' signals $F$ of an a priori known form $F (x) = \sum_{j = 1}^{d} a_{j} δ (x - x_{j}),$ from their moments $m_k(F)=\int x^kF…

math.CA2016

A case of multivariate Birkhoff interpolation using high order derivatives

Gil Goldman

We consider a specific scheme of multivariate Birkhoff polynomial interpolation. Our samples are derivatives of various orders $k_{j}$ at fixed points $v_{j}$ along fixed straight line…