On the accuracy of solving confluent prony systems

Dmitry Batenkov, Yosef Yomdin

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type." These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation and nonlinear Fourier inversion. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes critical for the success of any particular application. We investigate the question of "maximal possible accuracy" of solving Prony-type systems, putting stress on the "local" behavior which approximates situations with low absolute measurement error. The accuracy estimates are formulated in very simple geometric terms, shedding some light on the structure of the problem. Numerical tests suggest that "global" solution techniques such as Prony's algorithm and the ESPRIT method are suboptimal when compared to this theoretical "best local" behavior.

Original languageEnglish
Pages (from-to)134-154
Number of pages21
JournalSIAM Journal on Applied Mathematics
Volume73
Issue number1
DOIs
StatePublished - 2013

Keywords

  • Algebraic sampling
  • Confluent Prony system
  • Confluent Vandermonde matrix
  • ESPRIT
  • Frequency estimation
  • Hankel matrix
  • Jacobian determinant
  • PACE model
  • Prony method

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

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