ABSTRACT
This chapter explains the approaches aimed at analysis of inverse problems with uncertain data. A goal is to establish a technique for obtaining a posteriori estimates in inverse problems and provide its complete mathematical justification. The chapter considers the problem of recovery of unknown right‐hand sides of first‐order linear systems of ordinary differential equations with periodic boundary conditions from indirect observations of their solutions on a finite system of points and intervals. Under the assumption that right‐hand sides and deterministic errors in observations are subjected to some quadratic restrictions, the authors obtain a posteriori estimates of right‐hand sides which are compatible with observations data. Under some restrictions on unknown right‐hand sides of equations and errors in observations, the authors define the set consisting of those solutions and right‐hand sides of such equations which are compatible with observation data and then they choose the optimal solutions among them.
