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- W4300697749 abstract "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 connections with many different fields of Mathematics, stressing the role of Singularity Theory. We reformulate Prony System as the problem of reconstruction of Spike-train signals of the form $F(x)=sum_{j=1}^d a_jdelta(x-x_j)$ from the noisy moment measurements. We provide an overview of some recent results of [1-3, 6, 8, 9, 11, 12, 5] on the geometry of the error amplification in the reconstruction process, in situations where the nodes $x_j$ near-collide. Some algebraic-geometric structures, underlying the error amplification, are described (Prony, Vieta, and Hankel mappings, Prony varieties), as well as their connection with Vandermonde mappings and varieties. Our main goal is to present some promising fields of possible applications of Singulary Theory." @default.
- W4300697749 created "2022-10-04" @default.
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- W4300697749 date "2018-01-07" @default.
- W4300697749 modified "2023-10-18" @default.
- W4300697749 title "Accuracy of noisy Spike-Train Reconstruction: a Singularity Theory point of view" @default.
- W4300697749 doi "https://doi.org/10.48550/arxiv.1801.02177" @default.
- W4300697749 hasPublicationYear "2018" @default.
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