Weak limits of consecutive projections and of greedy steps

2021/12/09 by Borodin, Petr A., Kopecka, Eva
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2112.05094

Abstract

Let H be a Hilbert space. We investigate the properties of weak limit points of iterates of random projections onto K≥ 2 closed convex sets in H and the parallel properties of weak limit points of residuals of random greedy approximation with respect to K dictionaries. In the case of convex sets these properties imply weak convergence in all the cases known so far. In particular, we give a short proof of the theorem of Amemiya and Ando on weak convergence when the convex sets are subspaces. The question of the weak convergence in general remains open.

Related

• Convergence of remote projections onto convex sets
• Alternating projections, remotest projections, and greedy approximation
• Convergence of Random Products of Countably Infinitely Many Projections
• Unrestricted iterations of relaxed projections in Hilbert space: Regularity, absolute convergence, and statistics of displacements
• On Dykstra's algorithm: finite convergence, stalling, and the method of alternating projections