13 citations · 23 across the 9 of their papers we have counts for
6 papers · 1 filter
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…
Uniform upper bounds for the cyclicity of the zero solution of the Abel differential equation
Dmitry Batenkov, Gal Binyamini
Given two polynomials we consider the following question: "how large can the index of the first non-zero moment be, assuming the sequence is not…
Accuracy of spike-train Fourier reconstruction for colliding nodes
Andrey Akinshin, Dmitry Batenkov, Yosef Yomdin
We consider Fourier reconstruction problem for signals F, which are linear combinations of shifted delta-functions. We assume the Fourier transform of F to be known on the frequenc…
Taylor Domination, Difference Equations, and Bautin Ideals
Dmitry Batenkov, Yosef Yomdin
We compare three approaches to studying the behavior of an analytic function from its Taylor coefficients. The first is "Taylor domination" property…
Moment vanishing of piecewise solutions of linear ODEs
Dmitry Batenkov, Gal Binyamini
We consider the "moment vanishing problem" for a general class of piecewise-analytic functions which satisfy on each continuity interval a linear ODE with polynomial coefficients.…
Moment inversion problem for piecewise D-finite functions
Dmitry Batenkov
We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an…