A convergence analysis of iterative methods for the solution of nonlinear ill-posed problems under affinely invariant conditions

Abstract

For iterative methods for well-posed problems, invariance properties have been used to provide a unified framework for convergence analysis. We carry over this approach to iterative methods for nonlinear ill-posed problems and prove convergence with rates for the Landweber and the iteratively regularized Gauss-Newton methods. The conditions needed are weaker as far as the nonlinearity is concerned than those needed in earlier papers and apply also to severely ill-posed problems. With no additional effort, we can also treat multilevel versions of our methods.