56 citations · 196 across the 25 of their papers we have counts for
14 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…
Accuracy of Algebraic Fourier Reconstruction for Shifts of Several Signals
Dmitry Batenkov, Niv Sarig, Yosef Yomdin
We consider the problem of "algebraic reconstruction" of linear combinations of shifts of several known signals from the Fourier samples. Following \cite{Bat.Sar.Y…
Sampling, Metric Entropy and Dimensionality Reduction
D. Batenkov, O. Friedland, Y. Yomdin
Let be a relatively compact subset in a Hilbert space . For a given $\e>0$ let $N(\e,Q)$ be the minimal number of linear measurements, sufficient to reconstruct any $x \in Q…
Decoupling of Fourier Reconstruction System for Shifts of Several Signals
Dmitry Batenkov, Niv Sarig, Yosef Yomdin
We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals from the Fourier samples. For each we ch…
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.…
Taylor Domination, Turán lemma, and Poincaré-Perron Sequences
Dmitry Batenkov, Yosef Yomdin
We consider "Taylor domination" property for an analytic function in the complex disk , which is an inequality of the form \[ |a_{k}|R^{k…
Reconstruction of Planar Domains from Partial Integral Measurements
Dmitry Batenkov, Vladimir Golubyatnikov, Yosef Yomdin
We consider the problem of reconstruction of planar domains from their moments. Specifically, we consider domains with boundary which can be represented by a union of a finite numb…
On the accuracy of solving confluent Prony systems
Dmitry Batenkov, Yosef Yomdin
In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branc…
Algebraic reconstruction of piecewise-smooth functions from integral measurements
Dmitry Batenkov, Niv Sarig, Yosef Yomdin
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from t…
Algebraic Fourier reconstruction of piecewise smooth functions
Dmitry Batenkov, Yosef Yomdin
Accurate reconstruction of piecewise-smooth functions from a finite number of Fourier coefficients is an important problem in various applications. The inherent inaccuracy, in part…
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…