A posteriori parameter choice with an efficient discretization scheme for solving ill-posed problems (Q2518672)

The paper deals with optimal \textit{a-posteriori} parameter choice strategies for Tikhonov regularization for solving ill--posed inverse problems in a \textit{finite} dimensional setting. Thereby optimal a-posteriori strategies from \textit{H.-W. Engl} and \textit{H. Gfrerer} [Appl. Numer. Math. 4, No. 5, 395--417 (1988; Zbl 0647.65038)] (see also \textit{A. Neubauer}, Appl. Numer. Math. 4, No. 6, 507--519 (1988; Zbl 0698.65032)]), developed for the infinite dimensional setting, serve as a starting point. The goal of this paper is to incorporate into the parameter choice strategy the discretization in an optimal way. In this way the parameter selection criterion reveals an additional term, which finally allows to optimally select a discretization.