On adaptive discretization schemes for the regularization of ill-posed problems with semiiterative methods

TL;DR

This paper proposes an adaptive discretization approach combined with semiiterative regularization methods for ill-posed linear problems, achieving order optimality and reduced computational costs.

Contribution

It introduces a novel adaptive discretization strategy that, together with established stopping rules, enhances regularization efficiency for ill-posed problems.

Findings

Order optimal regularization achieved

Reduced computational costs demonstrated

Effective with discrepancy and balancing principles

Abstract

In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a stopping criterion as the discrepancy principle or the balancing principle yields an order optimal regularization scheme and allows to reduce the computational costs.