The rate of convergence in the method of alternating projections
Functional Analysis
2012-09-06 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1006.2047,
title = {The rate of convergence in the method of alternating projections},
author = {Catalin Badea and Sophie Grivaux and Vladimir Muller},
journal= {arXiv preprint arXiv:1006.2047},
year = {2012}
}
Comments
23 pages, to appear in St. Petersburg Math J. (2010)