Geometry and Singularities of the Prony mapping

DOI10.5427/jsing.2014.10azbMath1353.94014arXiv1301.1336OpenAlexW2963560677MaRDI QIDQ2941098

Yosef Yomdin, Dmitry Batenkov

Publication date: 22 January 2015

Published in: Journal of Singularities (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.1336

zbMATH Keywords

singularitiesnon-linear modelssignal acquisitionmoments inversion

Mathematics Subject Classification ID

General nonlinear regression (62J02) Signal theory (characterization, reconstruction, filtering, etc.) (94A12)

Related Items (12)

Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view ⋮ Learning algebraic decompositions using Prony structures ⋮ Local and Global Geometry of Prony Systems and Fourier Reconstruction of Piecewise-Smooth Functions ⋮ Geometry of error amplification in solving the Prony system with near-colliding nodes ⋮ The spectral properties of Vandermonde matrices with clustered nodes ⋮ Smooth parametrizations in dynamics, analysis, diophantine and computational geometry ⋮ Stable soft extrapolation of entire functions ⋮ On algebraic properties of low rank approximations of Prony systems ⋮ Stability and super-resolution of generalized spike recovery ⋮ Accuracy of reconstruction of spike-trains with two near-colliding nodes ⋮ Complete algebraic reconstruction of piecewise-smooth functions from Fourier data ⋮ Accurate solution of near-colliding Prony systems via decimation and homotopy continuation

Cites Work

• Prony systems via decimation and homotopy continuation
• Performance of ESPRIT for Estimating Mixtures of Complex Exponentials Modulated by Polynomials
• On the Accuracy of Solving Confluent Prony Systems
• Complete algebraic reconstruction of piecewise-smooth functions from Fourier data
• Towards a Mathematical Theory of Super‐resolution

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