On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems
For solving the nonlinear ill-posed problem \(F(x)= y\), where \(F\) is a weakly closed, continuous and Fréchet differentiable operator between Hilbert spaces, Tikhonov's regularization is well known. \textit{O. Scherzer}, \textit{H. W. Engl} and \textit{K. Kunisch} [SIAM J. Numer. Anal. 30, No. 6, 1796-1838 (1993; Zbl 0799.65060)] proposed an a posteriori technique to find optimal regularization parameters. Unfortunately, assumptions for proving optimally were too restrictive to cover a larger set of problems. In this paper, the authors proceed with the study of the technique proposed and prove optimality under less restrictive conditions. Moreover, convergence rates could be improved.
scientific article; zbMATH DE number 1355489