On inertial iterated Tikhonov methods for solving ill-posed problems

Abstract

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.