Abstract
So-called local a posteriori accuracy estimates for approximate solutions of ill-posed inverse problems are under investigation. We present an approach to local a posteriori estimation along with the numerical algorithm for calculating the estimators. We analyze the local optimality in order of obtained a posteriori accuracy estimates and introduce a new important notion of locally extra-optimal regularizing algorithm as a method for the solution of ill-posed problems having optimal in order local a posteriori accuracy estimates. Finally, we demonstrate the results of numerical experiments on applications of locally extra-optimal regularizing methods, constructed on the base of Tikhonov regularization, for calculating local a posteriori accuracy estimates.
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 11-01-00040-a
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 12-01-91153-GFEN-a
© 2014 by De Gruyter
