Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
Functional Analysis
2015-11-11 v1 Numerical Analysis
Abstract
In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.
Keywords
Cite
@article{arxiv.1511.02950,
title = {Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces},
author = {Vinicius Albani and Peter Elbau and Maarten V. de Hoop and Otmar Scherzer},
journal= {arXiv preprint arXiv:1511.02950},
year = {2015}
}