Abstract

The preconditioned iteratively regularized Gauss–Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (Inverse Problems 23: 1547–1563, 2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes ℳ-times iterated Tikhonov regularization with line search. Numerical schemes illustrating the theoretical results are also presented.