Alternating Projections on Nontangential Manifolds
(2013) In Constructive Approximation 38(3). p.489-525- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4204312
- author
- Andersson, Fredrik LU and Carlsson, Marcus LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Alternating projections, Convergence, Non-convexity, Low-rank, approximation, Manifolds
- in
- Constructive Approximation
- volume
- 38
- issue
- 3
- pages
- 489 - 525
- publisher
- Springer
- external identifiers
-
- wos:000326347600006
- scopus:84886801436
- ISSN
- 0176-4276
- DOI
- 10.1007/s00365-013-9213-3
- language
- English
- LU publication?
- yes
- id
- 79ef41bf-efe1-47d7-a093-23f0ddebd25f (old id 4204312)
- date added to LUP
- 2016-04-01 11:07:17
- date last changed
- 2022-05-18 08:31:54
@article{79ef41bf-efe1-47d7-a093-23f0ddebd25f,
abstract = {{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.}},
author = {{Andersson, Fredrik and Carlsson, Marcus}},
issn = {{0176-4276}},
keywords = {{Alternating projections; Convergence; Non-convexity; Low-rank; approximation; Manifolds}},
language = {{eng}},
number = {{3}},
pages = {{489--525}},
publisher = {{Springer}},
series = {{Constructive Approximation}},
title = {{Alternating Projections on Nontangential Manifolds}},
url = {{http://dx.doi.org/10.1007/s00365-013-9213-3}},
doi = {{10.1007/s00365-013-9213-3}},
volume = {{38}},
year = {{2013}},
}