Angle criteria for uniform convergence of averaged projections and cyclic or random products of projections

TL;DR

This paper introduces a new angle-based approach to establish uniform convergence criteria for various projection methods, including averaged, cyclic, quasi-periodic, and random projections, enhancing understanding of their convergence behavior.

Contribution

It proposes a novel angle concept between projections to derive convergence criteria across multiple projection algorithms, extending previous theoretical frameworks.

Findings

Established convergence criteria for averaged projections

Derived conditions for cyclic and quasi-periodic products

Extended results to random projection products

Abstract

We apply a new notion of angle between projections to deduce criteria for uniform convergence results of the alternating projections method under several different settings: averaged projections, cyclic products, quasi-periodic products and random products.