Embedded techniques for choosing the parameter in Tikhonov regularization
Numerical Analysis
2013-07-02 v1
Abstract
This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy principle, although no initial knowledge of the norm of the error that affects the right-hand side is assumed; an increasingly more accurate approximation of this quantity is recovered during the Arnoldi algorithm. Some theoretical estimates are derived in order to motivate our approach. Many numerical experiments, performed on classical test problems as well as image deblurring are presented.
Cite
@article{arxiv.1307.0334,
title = {Embedded techniques for choosing the parameter in Tikhonov regularization},
author = {Silvia Gazzola and Paolo Novati and Maria Rosaria Russo},
journal= {arXiv preprint arXiv:1307.0334},
year = {2013}
}