Prony systems via decimation and homotopy continuation

We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recently discovered "decimation" technique, we present an algorithm which applies homotopy continuation on a sequence of modified Hankel-type systems as above. In this way, we are able to solve for the nonlinear variables of the original system with high accuracy when the data is perturbed.