The rate of convergence for the cyclic projections algorithm I: Angles between convex sets

JOURNAL OF APPROXIMATION THEORY

卷:142

Article

Deutsch, Frank ; Hundal, Hein

关键词: convex feasibility problem;    cyclic projections algorithm;    rate of convergence;    projections onto convex sets;    POCS;    alternating projections;    orthogonal projections;    angle between convex sets;    angle between subspaces;   

DOI  :  10.1016/j.jat.2006.02.005

来源: Elsevier

【 摘 要 】

The cyclic projections algorithm is an important method for determining a point in the intersection of a finite number of closed convex sets in a Hilbert space. That is, for determining a solution to the convex feasibility problem. We study the rate of convergence for the cyclic projections algorithm. The notion of angle between convex sets is defined, which generalizes the angle between linear subspaces. The rate of convergence results are described in terms of these angles. (C) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free