Accelerating The Convergence Of The Method Of Alternating Projections (1999)
| Venue: | Trans. Amer. Math. Soc |
| Citations: | 6 - 1 self |
BibTeX
@ARTICLE{Bauschke99acceleratingthe,
author = {Heinz H. Bauschke and Frank Deutsch and Hein Hundal and Sung-Ho Park},
title = {Accelerating The Convergence Of The Method Of Alternating Projections},
journal = {Trans. Amer. Math. Soc},
year = {1999},
volume = {355},
pages = {3433--3461}
}
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Abstract
. The powerful von Neumann-Halperin method of alternating projections (MAP) is an algorithm for determining the best approximation to any given point in a Hilbert space from the intersection of a nite number of subspaces. It achieves this by reducing the problem to an iterative scheme which involves only computing best approximations from the individual subspaces which make up the intersection. The main practical drawback of this algorithm, at least for some applications, is that the method is slowly convergent. In this paper, we consider a general class of iterative methods which includes the MAP as a special case. For such methods, we study an \accelerated" version of this algorithm which was considered earlier by Gubin, Polyak, and Raik [14] and by Gearhart and Koshy [13]. We show that the accelerated algorithm converges faster than the MAP in the case of two subspaces, but is in general not faster than the MAP for more than two subspaces! However, for a \symmetric" version of the ...
