Accurate solution of near-colliding Prony systems via decimation and homotopy continuation

Dmitry Batenkov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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 consider a case when the structure of the system is a-priori fixed. 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 to an appropriately chosen Hankel-type system 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.

Original languageEnglish
Pages (from-to)27-40
Number of pages14
JournalTheoretical Computer Science
Volume681
DOIs
StatePublished - 12 Jun 2017
Externally publishedYes

Keywords

  • Decimation
  • ESPRIT
  • Homotopy continuation
  • Polynomial systems
  • Prony system

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