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arXiv · 2401.15213

On inertial iterated Tikhonov methods for solving ill-posed problems

Joel C. Rabelo·Antonio Leitão·Alexandre L. Madureira
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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.

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Joel C. Rabelo, Antonio Leitão, Alexandre L. Madureira. 2024-01-26. On inertial iterated Tikhonov methods for solving ill-posed problems. https://arxiv.org/abs/2401.15213

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