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Licensed Unlicensed Requires Authentication Published by De Gruyter November 30, 2016

On Nesterov acceleration for Landweber iteration of linear ill-posed problems

Andreas Neubauer

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((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.

MSC 2010: 47A52; 65J20; 65R30

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Received: 2016-9-15
Accepted: 2016-11-5
Published Online: 2016-11-30
Published in Print: 2017-6-1

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