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- Title
OBSERVATIONS ON THE METRIC PROJECTION IN FINITE DIMENSIONAL BANACH SPACES.
- Authors
BARGETZ, CHRISTIAN; LUGGIN, FRANZ
- Abstract
We consider the method of alternating (metric) projections for pairs of linear subspaces of finite dimensional Banach spaces. We investigate the size of the set of points for which this method converges to the metric projection onto the intersection of these subspaces. In addition, we give a characterisation of the pairs of subspaces for which the alternating projection method converges to the projection onto the intersection for every initial point. We provide a characterisation of the linear subspaces of lnp, 1 < p < ∞, p ≠ 2, which admit a linear metric projection and use this characterisation to show that in l³p, 1 < p < ∞, p ≠ 2, the set of pairs of subspaces for which the alternating projection method converges to the projection onto the intersection is small in a probabilistic sense.
- Subjects
METRIC projections; BANACH spaces; SET theory; PROBABILITY theory; SUBSPACES (Mathematics)
- Publication
Applied Set-Valued Analysis & Optimization, 2024, Vol 6, Issue 1, p41
- ISSN
2562-7775
- Publication type
Article
- DOI
10.23952/asvao.6.2024.1.04