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: | Lewis Adrian S, Malick Jrme |
Keywords: | sets, matrices |
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.