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On Local Convergence of the Method of Alternating Projections

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Abstract

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets \(A,B\) under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is \({\mathcal {O}}(k^{-\rho })\) for some \(\rho \in (0,\infty )\).

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Authors and Affiliations

  1. Institut de Mathématiques, Université de Toulouse, 118, route de Narbonne, 31062, Toulouse, France

    Dominikus Noll & Aude Rondepierre

  2. Institut de Mathématiques, INSA Toulouse, Toulouse, France

    Aude Rondepierre

Authors
  1. Dominikus Noll
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  2. Aude Rondepierre
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Correspondence to Dominikus Noll.

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Communicated by Michael Todd.

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Noll, D., Rondepierre, A. On Local Convergence of the Method of Alternating Projections. Found Comput Math 16, 425–455 (2016). https://doi.org/10.1007/s10208-015-9253-0

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  • DOI: https://doi.org/10.1007/s10208-015-9253-0

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