Uniform convergence of regularization methods for linear ill-posed problems

Authors: Heinz W. Engl and Günther Hodina

Abstract: After a general discussion about convergence and convergence rates for regularization methos in Banach spaces, we present a general method that can be used to modify regularization methods in L^2 in such a way that uniform convergence, which is often preferred in concrete applications to just L^2-convergence, is obtained. We prove results about convergence rates in the uniform norm and discuss questions of parameter choice. The theoretical results will be supported by numerical examples, which indicate that although the results are asymtotic in character, they are of some relevance also for actual computations.