Abstract

In this paper we investigate the numerical complexity to solve nonlinear ill-posed problems when the operator equations F(x) = y^δ are solved by the iteratively regularized Gauss–Newton method (IRGNM) with inner CG-iteration. Additionally we consider a preconditioned version of the IRGNM and compare the complexity of the standard IRGNM and its preconditioned version. In the case of exponentially ill-posed problems we show the superiority of the preconditioned IRGNM, that is we prove that the preconditioning techniques presented in this paper yield a significant reduction of the total complexity.