This is an announcement for the paper "The rate of convergence in the method of alternating projections" by Catalin Badea, Sophie Grivaux and Vladimir Muller.

Abstract: 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.

Archive classification: math.FA math.NA

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

Submitted from: catalin.badea@math.univ-lille1.fr

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1006.2047

or

http://arXiv.org/abs/1006.2047