Characterizing arbitrarily slow convergence in the method of alternating projections
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...
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| Veröffentlicht in: | International transactions in operational research 2009-07, Vol.16 (4), p.413-425 |
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| creator | Bauschke, Heinz H. Deutsch, Frank Hundal, Hein |
| description | 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. |
| doi_str_mv | 10.1111/j.1475-3995.2008.00682.x |
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| ispartof | International transactions in operational research, 2009-07, Vol.16 (4), p.413-425 |
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| language | eng |
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| subjects | alternating projections angle between subspaces cyclic projections Errors Hilbert space Operations research orthogonal projections rate of convergence of the method of alternating projections Studies Theorems |
| title | Characterizing arbitrarily slow convergence in the method of alternating projections |
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