Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres
Functional Analysis
2018-09-18 v3
Abstract
We expand upon previous work that examined behavior of the iterated Douglas-Rachford method for a line and a circle by considering two generalizations: that of a line and an ellipse and that of a line together with a -sphere. With computer assistance we discover a beautiful geometry that illustrates phenomena which may affect the behavior of the iterates by slowing or inhibiting convergence for feasible cases. We prove local convergence near feasible points, and---seeking a better understanding of the behavior---we employ parallelization in order to study behavior graphically. Motivated by the computer-assisted discoveries, we prove a result about behavior of the method in infeasible cases.
Cite
@article{arxiv.1610.03975,
title = {Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres},
author = {Jonathan M. Borwein and Scott B. Lindstrom and Brailey Sims and Anna Schneider and Matthew P. Skerritt},
journal= {arXiv preprint arXiv:1610.03975},
year = {2018}
}