Alternating Projections on Nontangential Manifolds

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.

• Författare: Fredrik Andersson; Marcus Carlsson
• Avdelning/ar: Matematik LTH; Matematik (naturvetenskapliga fakulteten); ELLIIT: the Linköping-Lund initiative on IT and mobile communication; eSSENCE: The e-Science Collaboration
• Publiceringsår: 2013
• Språk: Engelska
• Sidor: 489-525
• Publikation/Tidskrift/Serie: Constructive Approximation
• Volym: 38
• Issue: 3
• Länkar: http://dx.doi.org/10.1007/s00365-013-9213-3
• Dokumenttyp: Artikel i tidskrift
• Förlag: Springer
• Ämne: Mathematics
• Nyckelord: Alternating projections; Convergence; Non-convexity; Low-rank; approximation; Manifolds
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 0176-4276