Using variable Hilbert scales setting we study the following questions:
1) Which ill-posed problems can be treated with optimal accuracy by standard regularization techniques such as Tikhonov
regularization, Landweber iterations and so on?
2) Is there adaptive strategy for choosing regularization parameter which guarantee the best order of accuracy for fixed
regularization method without use the knowledge of the solution smoothness?
3) What is the minimal amount of noisy discrete information that allows to solve ill-posed problems with optimal accuracy
under general source condition?
Copyright. All Rights Reserved.