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Non-optimality of the Greedy Algorithm for subspace orderings in the method of alternating projections

Abstract:

The method of alternating projections involves projecting an element of a Hilbert space cyclically onto a collection of closed subspaces. It is known that the resulting sequence always converges in norm and that one can obtain estimates for the rate of convergence in terms of quantities describing the geometric relationship between the subspaces in question, namely their pairwise Friedrichs numbers. We consider the question of how best to order a given collection of subspaces so as to obtain ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1007/s00025-017-0721-5

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Institute
Role:
Author
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Publisher:
Springer Verlag Publisher's website
Journal:
Results in Mathematics Journal website
Volume:
72
Issue:
1-2
Pages:
979–990
Publication date:
2017-07-14
Acceptance date:
2017-06-28
DOI:
EISSN:
1420-9012
ISSN:
1422-6383
Pubs id:
pubs:702134
URN:
uri:bdebead7-9268-4296-88be-5178dfccae91
UUID:
uuid:bdebead7-9268-4296-88be-5178dfccae91
Local pid:
pubs:702134
Paper number:
1-2

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