Algebraic Geometry of Error Amplification: the Prony leaves
Dmitry Batenkov, Gil Goldman, Yehonatan Salman, Yosef Yomdin · arXiv (Cornell University) · 2017
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" $S_q$, whose leaves are "equi-moment surfaces" in the parameter space. Next, we prove some new results concerning explicit parametrization of the Prony leaves.