Characterizing arbitrarily slow convergence in the method of alternating projections

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dc.creatorBauschke, H. H.
dc.creatorDeutsch, F.
dc.creatorHundal, H.
dc.date2007-10-12
dc.date.accessioned2026-07-07T08:35:57Z
dc.date.available2026-07-07T08:35:57Z
dc.descriptionIn 1997, Bauschke, Borwein, and Lewis have stated a trichotomy theorem that characterizes when the convergence of the method of alternating projections can be arbitrarily slow. However, there are two errors in their proof of this theorem. In this note, we show that although one of the errors is critical, the theorem itself is correct. We give a different proof that uses the multiplicative form of the spectral theorem, and the theorem holds in any real or complex Hilbert space, not just in a real Hilbert space.
dc.identifierhttps://arxiv.org/abs/0710.2387
dc.identifierhttp://arxiv.org/abs/0710.2387
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139910
dc.subjectFunctional Analysis
dc.subjectOptimization and Control
dc.subject47B20
dc.titleCharacterizing arbitrarily slow convergence in the method of alternating projections
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