A New Algorithm for a Posteriori Error Estimation for Approximate Solutions of Linear Ill-Posed Problems

Abstract

A new algorithm for a posteriori estimation of the error in solutions to linear operator equations of the first kind in a Hilbert space is proposed and justified. The algorithm reduces the variational problem of a posteriori error estimation to two special problems of maximizing smooth functionals under smooth constraints. A finite-dimensional version of the algorithm is considered. The results of a numerical experiment concerning a posteriori error estimation for a typical inverse problem are presented. It is shown experimentally that the computation time required by the algorithm is less, on average, by a factor of 1.4 than in earlier proposed methods.