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Characterizing arbitrarily slow convergence in the method of alternating projections
Author(s) -
Bauschke Heinz H.,
Deutsch Frank,
Hundal Hein
Publication year - 2009
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/j.1475-3995.2008.00682.x
Subject(s) - mathematics , hilbert space , multiplicative function , trichotomy (philosophy) , convergence (economics) , dominated convergence theorem , pure mathematics , mathematical analysis , compact convergence , rate of convergence , computer science , computer network , philosophy , linguistics , channel (broadcasting) , economics , economic growth
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.