Algebraic Geometry of Error Amplification: the Prony leaves
Classical Analysis and ODEs
2017-02-20 v1
Abstract
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 the "Prony foliations" , whose leaves are "equi-moment surfaces" in the parameter space. Next, we prove some new results concerning explicit parametrization of the Prony leaves.
Cite
@article{arxiv.1702.05338,
title = {Algebraic Geometry of Error Amplification: the Prony leaves},
author = {Dmitry Batenkov and Gil Goldman and Yehonatan Salman and Yosef Yomdin},
journal= {arXiv preprint arXiv:1702.05338},
year = {2017}
}