The rate of convergence in the method of alternating projections
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- by C. Badea, S. Grivaux and V. Müller
- St. Petersburg Math. J. 23 (2012), 413-434
- DOI: https://doi.org/10.1090/S1061-0022-2012-01202-1
- Published electronically: March 2, 2012
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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.References
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Bibliographic 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
- MR Author ID: 705957
- 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
- 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
- © Copyright 2012 American Mathematical Society
- 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
- MathSciNet review: 2896163