Semi-Heuristic Parameter Choice Rules for Tikhonov Regularisation with Operator Perturbations
Numerical Analysis
2018-07-16 v1
Abstract
We study the choice of the regularisation parameter for linear ill-posed problems in the presence of data noise and operator perturbations, for which a bound on the operator error is known but the data noise-level is unknown. We introduce a new family of semi-heuristic parameter choice rules that can be used in the stated scenario. We prove convergence of the new rules and provide numerical experiments that indicate an improvement compared to standard heuristic rules.
Cite
@article{arxiv.1807.05042,
title = {Semi-Heuristic Parameter Choice Rules for Tikhonov Regularisation with Operator Perturbations},
author = {Uno Hämarik and Urve Kangro and Stefan Kindermann and Kemal Raik},
journal= {arXiv preprint arXiv:1807.05042},
year = {2018}
}
Comments
21 pages, 6 figures, will be presented at the Chemnitz Symposium on Inverse Problems 2018