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On the convergence of von Neumann's alternating projection algorithm for two sets

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Abstract

We give several unifying results, interpretations, and examples regarding the convergence of the von Neumann alternating projection algorithm for two arbitrary closed convex nonempty subsets of a Hilbert space. Our research is formulated within the framework of Fejér monotonicity, convex and set-valued analysis. We also discuss the case of finitely many sets.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and Computing Science, Dalhousie University, B3H 3J5, Halifax, Nova Scotia, Canada

    H. H. Bauschke

  2. Department of Mathematics and Statistics, Simon Fraser University, V5A 1S6, Burnaby, British Columbia, Canada

    J. M. Borwein

Authors
  1. H. H. Bauschke
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  2. J. M. Borwein
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Bauschke, H.H., Borwein, J.M. On the convergence of von Neumann's alternating projection algorithm for two sets. Set-Valued Anal 1, 185–212 (1993). https://doi.org/10.1007/BF01027691

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