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Algebra i Analiz, 2011, Volume 23, Issue 3, Pages 1–30 (Mi aa1241)  
This article is cited in 30 scientific papers (total in 30 papers)

Research Papers

The rate of convergence in the method of alternating projections

C. Badeaa, S. Grivauxa, V. Müllerb

a Laboratoire Paul Painlevé, Université Lille 1, CNRS UMR 8524, Villeneuve d'Ascq, France
b Institute of Mathematics AV CR, Prague, Czech Republic
Full-text PDF (326 kB) Citations (30)
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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.
Keywords: Friedrichs angle, method of alternating projections, arbitrary slow convergence.
Received: 25.10.2009
English version:
St. Petersburg Mathematical Journal, 2012, Volume 23, Issue 3, Pages 413–434
DOI: https://doi.org/10.1090/S1061-0022-2012-01202-1
Bibliographic databases:
Document Type: Article
Language: English
Citation: C. Badea, S. Grivaux, V. Müller, “The rate of convergence in the method of alternating projections”, Algebra i Analiz, 23:3 (2011), 1–30; St. Petersburg Math. J., 23:3 (2012), 413–434
Citation in format AMSBIB
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    • This publication is cited in the following 30 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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    References:57
    First page:11
     
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