TY - JOUR

T1 - On Local Stability in the Complete Prony Problem

AU - Lomov, A. A.

N1 - The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0008).

PY - 2024/6

Y1 - 2024/6

N2 - Abstract: We consider the variational Prony problem on approximating observations by the sum of exponentials. We find critical pointsand the second derivatives of the implicit function that relates perturbation in with the corresponding exponents. We suggestupper bounds for the second order increments and describe the domain, where the accuracy ofa linear approximation of is acceptable.We deduce lower estimates of the norm of deviation of for small perturbations in. We compare our estimates of this norm withupper bounds obtained with the use of Wilkinson’s inequality.

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

KW - difference equation

KW - local stability

KW - parameter identification

KW - variational Prony problem

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85195181359&origin=inward&txGid=3c5c95177124c066d98e9ec5fecf287f

UR - https://www.mendeley.com/catalogue/a9b801bd-3bee-385a-8766-2a113a17de21/

U2 - 10.1134/S1055134424020044

DO - 10.1134/S1055134424020044

M3 - Article

VL - 34

SP - 116

EP - 145

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 2

ER -