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arXiv · 1910.01811

The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius

Barbara Kaltenbacher·Andrej Klassen·Mario Luiz Previatti de Souza
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Abstract

In this paper we consider the iteratively regularized Gauss-Newton method, where regularization is achieved by Ivanov regularization, i.e., by imposing a priori constraints on the solution. We propose an a posteriori choice of the regularization radius, based on an inexact Newton / discrepancy principle approach, prove convergence and convergence rates under a variational source condition as the noise level tends to zero, and provide an analysis of the discretization error. Our results are valid in general, possibly nonreflexive Banach spaces, including, e.g., $L^\infty$ as a preimage space. The theoretical findings are illustrated by numerical experiments.

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Barbara Kaltenbacher, Andrej Klassen, Mario Luiz Previatti de Souza. 2019-10-04. The Ivanov regularized Gauss-Newton method in Banach space with an a posteriori choice of the regularization radius. https://arxiv.org/abs/1910.01811

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