A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems
Numerical Analysis
2019-04-04 v1
Abstract
We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study 'Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales'. Inverse Problems 34(1), 2018, by the same authors. Optimal order convergence rates are established for the specific a priori parameter choice, as used for the corresponding linear equations.
Cite
@article{arxiv.1904.02014,
title = {A priori parameter choice in Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems},
author = {Bernd Hofmann and Peter Mathé},
journal= {arXiv preprint arXiv:1904.02014},
year = {2019}
}