The rate of convergence in the method of alternating projections

Catalin Badea (1, 2) , Sophie Grivaux (3, 1) , Vladimir Müller

1 Université de Lille
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 CNRS - Centre National de la Recherche Scientifique

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.

Domaines: Analyse fonctionnelle [math.FA]

Catalin Badea, Sophie Grivaux, Vladimir Müller. The rate of convergence in the method of alternating projections. St. Petersburg Mathematical Journal, 2012, 23 (3), pp.413-434. ⟨10.1090/S1061-0022-2012-01202-1⟩. ⟨hal-03494696⟩