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# Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

IMPACT FACTOR 2017: 0.941
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1569-3945
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# On Nesterov acceleration for Landweber iteration of linear ill-posed problems

Andreas Neubauer
Published Online: 2016-11-30 | DOI: https://doi.org/10.1515/jiip-2016-0060

## Abstract

In this paper we deal with Nesterov acceleration and show that it speeds up Landweber iteration when applied to linear ill-posed problems. It is proven that, if the exact solution ${x}^{†}\in \mathcal{ℛ}\left({\left({T}^{*}T\right)}^{\mu }\right)$, then optimal convergence rates are obtained if $\mu \le \frac{1}{2}$ and if the iteration is terminated according to an a priori stopping rule. If $\mu >\frac{1}{2}$ or if the iteration is terminated according to the discrepancy principle, only suboptimal convergence rates can be guaranteed. Nevertheless, the number of iterations for Nesterov acceleration is always much smaller if the dimension of the problem is large. Numerical results verify the theoretical ones.

MSC 2010: 47A52; 65J20; 65R30

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## About the article

Received: 2016-09-15

Accepted: 2016-11-05

Published Online: 2016-11-30

Published in Print: 2017-06-01

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 25, Issue 3, Pages 381–390, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219,

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© 2017 Walter de Gruyter GmbH, Berlin/Boston.

## Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Simon Hubmer and Ronny Ramlau
Inverse Problems, 2018, Volume 34, Number 9, Page 095003
[2]
Simon Hubmer, Ekaterina Sherina, Andreas Neubauer, and Otmar Scherzer
SIAM Journal on Imaging Sciences, 2018, Volume 11, Number 2, Page 1268
[3]
Simon Hubmer and Ronny Ramlau
Inverse Problems, 2017, Volume 33, Number 9, Page 095004

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