On inertial iterated Tikhonov methods for solving ill-posed problems
Numerical Analysis
2024-01-30 v1 Numerical Analysis
Abstract
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We establish convergence for exact data, and stability and semi-convergence for noisy data. Regarding numerical experiments we consider: i) a 2D Inverse Potential Problem, ii) an Image Deblurring Problem; the computational efficiency of the method is compared with standard implementations of the iT method.
Cite
@article{arxiv.2401.15213,
title = {On inertial iterated Tikhonov methods for solving ill-posed problems},
author = {Joel C. Rabelo and Antonio Leitão and Alexandre L. Madureira},
journal= {arXiv preprint arXiv:2401.15213},
year = {2024}
}
Comments
22 pages, 8 figures. Accepted for publication at Inverse Problems