Abstract
We consider the variational Prony problem on approximating observations \(x\) by the sum of exponentials. We find critical pointsand the second derivatives of the implicit function \(\theta\) that relates perturbation in \(x\) with the corresponding exponents. We suggestupper bounds for the second order increments and describe the domain, where the accuracy ofa linear approximation of \(\theta \) is acceptable.We deduce lower estimates of the norm of deviation of \(\theta\) for small perturbations in \(x\) . We compare our estimates of this norm withupper bounds obtained with the use of Wilkinson’s inequality.
