On pseudo-optimal parameter choice in Tikhonov regularization (Q2563386)

The problem of pseudo-optimal choice of the regularization parameter is stated. The author proposes an approach to choose the regularization parameter which ensures convergence of the Tikhonov approximation to the normal pseudo-solution of a linear operator equation of the first kind with perturbed operator and right hand side. This approach guarantees pseudo-optimality in the case of resolvency of the equation. It is a generalization of the approach of \textit{H. Gfrerer} [Math. Comput. 49, 507-522 (1987; Zbl 0631.65056)] for problems with unperturbed operators.