The rate of convergence in the method of alternating projections

Details The rate of convergence in the method of alternating projections The rate of convergence in the method of alternating projections

2010-06-10

arxiv.org/abs/1006.2047v1

Mathematics

Functional Analysis

23 pages, to appear in St. Petersburg Math J. (2010)

Scientific paper

A generalization of the cosine of the Friedrichs angle between two subspaces to a parameter associated to several closed subspaces of a Hilbert space is given. This parameter is used to analyze the rate of convergence in the von Neumann-Halperin method of cyclic alternating projections. General dichotomy theorems are proved, in the Hilbert or Banach space situation, providing conditions under which the alternative QUC/ASC (quick uniform convergence versus arbitrarily slow convergence) holds. Several meanings for ASC are proposed.

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