Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space

Barbara  Kaltenbacher; Ivan  Tomba

doi:10.3934/proc.2015.0686

Article Contents

2015, Volume 2015: 686-695. Doi: 10.3934/proc.2015.0686 open access

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Enhanced choice of the parameters in an iteratively regularized Newton-Landweber iteration in Banach space

Barbara Kaltenbacher^1, and
Ivan Tomba^2,

1.
Alpen-Adria-Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt
2.
Università di Bologna, Piazza Porta S. Donato, 5, 40127 - Bologna

Received: August 2014

Revised: June 2015

Published: November 2015

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Abstract

This paper is a close follow-up of [9] and [11], where Newton-Landweber iterations have been shown to converge either (unconditionally) without rates or (under an additional regularity assumption) with rates. The choice of the parameters in the method were different in each of these two cases. We now found a unified and more general strategy for choosing these parameters that enables both convergence and convergence rates. Moreover, as opposed to the previous one, this choice yields strong convergence as the noise level tends to zero, also in the case of no additional regularity. Additionally, the resulting method appears to be more efficient than the one from [9], as our numerical tests show.

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Mathematics Subject Classification: Primary: 65J20; Secondary: 65M32.

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References

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