Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations
Numerical Analysis
2020-12-23 v1 Numerical Analysis
Abstract
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the case of noisy data we propose a modification, the so called loping iterated Tikhonov-Kaczmarz method, where a sequence of relaxation parameters is introduced and a different stopping rule is used. Convergence analysis for this method is also provided.
Cite
@article{arxiv.2012.11985,
title = {Modified iterated Tikhonov methods for solving systems of nonlinear ill-posed equations},
author = {J. Baumeister and A. De Cezaro and A. Leitao},
journal= {arXiv preprint arXiv:2012.11985},
year = {2020}
}
Comments
18 pages. arXiv admin note: text overlap with arXiv:0801.3088, arXiv:2011.09674