In:
Journal of Inverse and Ill-posed Problems, Walter de Gruyter GmbH, Vol. 25, No. 3 ( 2017-6-1), p. 381-390
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 † ∈ ℛ ( ( T * T ) μ ) {x^{\dagger}\in{\cal R}((T^{*}T)^{\mu})} , then optimal convergence
rates are obtained if μ ≤ 1 2 {\mu\leq\frac{1}{2}} and if the iteration is terminated according
to an a priori stopping rule. If μ 〉 1 2 {\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.
Type of Medium:
Online Resource
ISSN:
0928-0219
,
1569-3945
DOI:
10.1515/jiip-2016-0060
Language:
English
Publisher:
Walter de Gruyter GmbH
Publication Date:
2017
detail.hit.zdb_id:
2041913-2
SSG:
11
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