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The rate of convergence in the method of alternating projections


Authors: C. Badea, S. Grivaux and V. Müller
Original publication: Algebra i Analiz, tom 23 (2011), nomer 3.
Journal: St. Petersburg Math. J. 23 (2012), 413-434
MSC (2010): Primary 47A05, 47A10, 41A35
DOI: https://doi.org/10.1090/S1061-0022-2012-01202-1
Published electronically: March 2, 2012
MathSciNet review: 2896163
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Abstract | References | Similar Articles | Additional Information

Abstract: The cosine of the Friedrichs angle between two subspaces is generalized to a parameter associated with several closed subspaces of a Hilbert space. This parameter is employed 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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Additional Information

C. Badea
Affiliation: Laboratoire Paul Painlevé, Université Lille 1, CNRS UMR 8524, 59655 Villeneuve d’Ascq, France
Email: badea@math.univ-lille1.fr

S. Grivaux
Affiliation: Laboratoire Paul Painlevé, Université Lille 1, CNRS UMR 8524, 59655 Villeneuve d’Ascq, France
Email: grivaux@math.univ-lille1.fr

V. Müller
Affiliation: Institute of Mathematics AV CR, Zitna 25, 115 67 Prague 1, Czech Republic
Email: muller@math.cas.cz

DOI: https://doi.org/10.1090/S1061-0022-2012-01202-1
Keywords: Friedrichs angle, method of alternating projections, arbitrarily slow convergence
Received by editor(s): October 25, 2009
Published electronically: March 2, 2012
Additional Notes: The first two authors were partially supported by ANR Project Blanc DYNOP. The third author was supported by grant No. 201/09/0473 of GA ČR and IAA100190903 of GA AV
Article copyright: © Copyright 2012 American Mathematical Society

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