Injectivity and weak*-to-weak continuity suffice for convergence rates in $\ell^1$-regularization
Functional Analysis
2017-01-16 v1 Numerical Analysis
Abstract
We show that the convergence rate of -regularization for linear ill-posed equations is always if the exact solution is sparse and if the considered operator is injective and weak*-to-weak continuous. Under the same assumptions convergence rates in case of non-sparse solutions are proven. The results base on the fact that certain source-type conditions used in the literature for proving convergence rates are automatically satisfied.
Cite
@article{arxiv.1701.03460,
title = {Injectivity and weak*-to-weak continuity suffice for convergence rates in $\ell^1$-regularization},
author = {Jens Flemming and Daniel Gerth},
journal= {arXiv preprint arXiv:1701.03460},
year = {2017}
}