A convergence analysis of regularization by discretization in preimage space

Kaltenbacher, Barbara; Offtermatt, Jonas

doi:10.1090/S0025-5718-2012-02596-8

A convergence analysis of regularization by discretization in preimage space
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by Barbara Kaltenbacher and Jonas Offtermatt PDF

Math. Comp. 81 (2012), 2049-2069 Request permission

Abstract:

In this paper we investigate the regularizing properties of discretization in preimage space for linear and nonlinear ill-posed operator equations with noisy data. We propose to choose the discretization level, that acts as a regularization parameter in this context, by a discrepancy principle. While general convergence has been shown not to hold, we provide convergence results under appropriate conditions on the exact solution.

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