Alternating Projections on Manifolds

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Alternating Projections on Manifolds
We prove that if two smooth manifolds intersect transversally, then the method of alternating projections converges locally at a linear rate. We bound the speed of convergence in terms of the angle between the manifolds, which in turn we relate to the modulus of metric regularity for the intersection problem, a natural measure of conditioning. We discuss a variety of problem classes where the projections are computationally tractable, and we illustrate the method numerically on a problem of finding a low-rank solution of a matrix equation. Key words: alternating projections, nonconvex, linear convergence, subspace angle, metric regularity, low-rank approximation, spectral set AMS 2000 Subject Classification: 49M29, 65K10, 90C30
Adrian S. Lewis, Jérôme Malick
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2008
Where MOR
Authors Adrian S. Lewis, Jérôme Malick
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