Parameter Choice Strategy Research Articles

Regularization of ill-posed problems: Optimal parameter choice in finite dimensions

We investigate a general class of regularization methods for ill-posed linear operator equations. An optimal a posteriori parameter choice strategy is developed for finite-dimensional approximations. The strategy is illustrated for a number of specific methods.

An optimal parameter choice for regularized ill-posed problems

Schock has given a nearly optimal a posteriori parameter choice strategy for Tikhonov regularization. We show that a modification of his argument leads, in fact, to an optimal convergence rate.

A posteriori parameter choice for general regularization methods for solving linear ill-posed problems

For continuous and iterative regularization methods for solving linear ill-posed problems, we propose an a posteriori parameter choice strategy and stopping rule, respectively, that always leads to optimal convergence rates and does not require the knowledge of the smoothness of the exact solution.

A parameter choice strategy for (iterated) tikhonov regularization of iii-posed problems leading to superconvergence with optimal rates

For ordinary and iterated Tikhonov regularization of linear ill-posed problems, we propose a parameter choice strategy that leads to optimal (super-) convergence rates for certain linear functionals of the regularized solution. It is not necessary to know the smoothness index of the exact solution; approximate knowledge of the smoothness index for the linear functional suffices