Linear Convergence Rates for Extrapolated Fixed Point Algorithms

TL;DR

This paper proves that certain extrapolated fixed point algorithms, including simultaneous and cyclic cutter methods, converge linearly in Hilbert spaces, with analysis covering metric and subgradient projections.

Contribution

It establishes the first linear convergence rates for a class of extrapolated fixed point algorithms based on dynamic string-averaging methods.

Findings

Linear convergence rates are proven for extrapolated fixed point algorithms.

Results apply to both metric and subgradient projections.

Includes analysis of extrapolated simultaneous and cyclic cutter methods.

Abstract

We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in particular, to the extrapolated simultaneous and cyclic cutter methods. Our analysis covers the cases of both metric and subgradient projections.