On Local Convergence of the Method of Alternating Projections

TLDR: In this article, the authors proved local convergence of alternating projections between subanalytic sets under a mild regularity hypothesis on one of the sets, and showed that the speed of convergence is O(k √ √ σ(k − σ ) for some constant σ √ n, σ (n) for some σ σ = (0, √ N) √ (n − ρ) for any σ > 0.

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 $$A,B$$A,B under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is $${\mathcal {O}}(k^{-\rho })$$O(k-?) for some $$\rho \in (0,\infty )$$??(0,?).