Regularization of linear and nonlinear ill-posed problems by mollification
Abstract
In this paper, we address the problem of approximating solutions of ill-posed problems using mollification. We quickly review existing mollification regularization methods and provide two new approximate solutions to a general ill-posed equation where can be nonlinear. The regularized solutions we define extend the work of Bonnefond and Mar\'echal \cite{xapi}, and trace their origins in the variational formulation of mollification, which to the best of our knowledge, was first introduced by Lannes et al. \cite{lannes}. In addition to consistency results, for the first time, we provide some convergence rates for a mollification method defined through a variational formulation.
Cite
@article{arxiv.2003.07913,
title = {Regularization of linear and nonlinear ill-posed problems by mollification},
author = {Walter Cedric Simo Tao Lee},
journal= {arXiv preprint arXiv:2003.07913},
year = {2020}
}
Comments
This paper is a premature version of a work performed while the author was a PhD student under the supervision of Pierre Mar\'echal and Anne Vanhems, at the University of Toulouse, and it benefited from the directions provided by them. The paper has to be re-written