On local stability in the complete Prony problem

The material was received by the Editorial Board: 09.10.2023

In the variational Prony problem of approximating observations x by the sum of exponentials, expressions are obtained for critical points and second derivatives of the implicit function θ(x) of exponents' dependence on x data. Upper bounds are proposed for the second order increments ||Δ2 θ|| with a description of the Δx area where θ(x) is approximately linear.  As a consequence, the lower bounds for ||Δθ|| are obtained for small perturbations in x.  A comparison with the upper bounds for ||Δθ|| by Wilkinson's inequality is given

УДК 517.962.22

Keywords: Difference equations, parameter identification, approximations by the sum of exponentials, variational Prony problem, local stability


References: Lomov A. A. On local stability in the complete Prony problem. Mat. Trudy. 2024, 27, № 1. P. 96–138. DOI: 10.25205/1560-750X-2024-27-1-96-138