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arXiv · 1406.4012

Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes

C. H. Jeffrey Pang
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Abstract

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.

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C. H. Jeffrey Pang. 2014-06-16. Accelerating the alternating projection algorithm for the case of affine subspaces using supporting hyperplanes. https://arxiv.org/abs/1406.4012

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