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Alternating Projections on Nontangential Manifolds

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Author

Summary, in English

We consider sequences of points obtained by projecting a given point B=B (0) back and forth between two manifolds and , and give conditions guaranteeing that the sequence converges to a limit . Our motivation is the study of algorithms based on finding the limit of such sequences, which have proved useful in a number of areas. The intersection is typically a set with desirable properties but for which there is no efficient method for finding the closest point B (opt) in . Under appropriate conditions, we prove not only that the sequence of alternating projections converges, but that the limit point is fairly close to B (opt) , in a manner relative to the distance ayenB (0)-B (opt) ayen, thereby significantly improving earlier results in the field.

Publishing year

2013

Language

English

Pages

489-525

Publication/Series

Constructive Approximation

Volume

38

Issue

3

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Keywords

  • Alternating projections
  • Convergence
  • Non-convexity
  • Low-rank
  • approximation
  • Manifolds

Status

Published

ISBN/ISSN/Other

  • ISSN: 0176-4276