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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 25, Issue 3


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


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((T*T)μ), then optimal convergence rates are obtained if μ12 and if the iteration is terminated according to an a priori stopping rule. If μ>12 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.

Keywords: Nesterov acceleration; Landweber iteration; linear ill-posed problems

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, DOI: https://doi.org/10.1515/jiip-2016-0060.

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