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Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes
The von Neumann-Halperin method of alternating projections converges strongly
to the projection of a given point onto the intersection of finitely many
closed affine subspaces. We propose acceleration schemes making use of two
ideas: Firstly, each projection onto an affine subspace identifies a hyperplane
of codimension 1 containing the intersection, and secondly, it is easy to
project onto a finite intersection of such hyperplanes. We give conditions for
which our accelerations converge strongly. Finally, we perform numerical
experiments to show that these accelerations perform well for a matrix model
updating problem.Comment: 16 pages, 3 figures (Corrected minor typos in Remark 2.2, Algorithm
2.5, proof of Theorem 3.12, as well as elaborated on certain proof
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