Alternating Projections on Manifolds

Alternating Projections on Manifolds

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Article ID: iaor200954155
Country: United States
Volume: 33
Issue: 1
Start Page Number: 216
End Page Number: 234
Publication Date: Feb 2008
Journal: Mathematics of Operations Research
Authors: ,
Keywords: sets, matrices
Abstract:

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.

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