On local stability in the complete Prony problem

Lomov Andrey Alexandrovich

0000-0001-5945-2923

Scopus Author ID: 57195387616

1. Sobolev Institute of Mathematics, Siberian Branch Russian Academy of Sciences, Novosibirsk, Russia

2. Novosibirsk State University, Novosibirsk, Russia

lomov@math.nsc.ru

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