Title

Moment Discretization For Ill-Posed Problems With Discrete Weakly Bounded Noise

Keywords

Discrete weakly bounded noise; Ill-posed problems; Moment discretization; Reproducing kernel Hilbert spaces; Tikhonov regularization

Abstract

We study moment discretization for compact operator equations in Hilbert space with discrete noisy data. Instead of assuming that the error in the data converges strongly to 0, we only assume weak convergence of the noise as introduced by Eggermont et al. (Inverse Probl 25:115018, 2009). A specific instance would be random noise. Under the usual source conditions, we derive optimal convergence rates for Phillips-Tikhonov regularization. The analysis is based on the comparison of the discrete problem with a semi-discrete version of the problem, which is made possible by virtue of a quadrature result in a suitable reproducing kernel Hilbert space. Some numerical results using strong and weak discrepancy principles for the selection of the regularization parameter are presented. © 2012 Springer-Verlag.

Publication Date

11-1-2012

Publication Title

GEM - International Journal on Geomathematics

Volume

3

Issue

2

Number of Pages

155-178

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s13137-012-0037-2

Socpus ID

84867483592 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84867483592

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