- Title
- Dynamics of the Douglas-Rachford method for ellipses and p-spheres
- Creator
- Borwein, Jonathan M.; Lindstrom, Scott B.; Sims, Brailey; Schneider, Anna; Skerritt, Matthew P.
- Relation
- Set-Valued and Variational Analysis Vol. 26, Issue 2, p. 385-403
- Publisher Link
- http://dx.doi.org/10.1007/s11228-017-0457-0
- Publisher
- Springer
- Resource Type
- journal article
- Date
- 2018
- Description
- We expand upon previous work that examined the 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 p-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.
- Subject
- Douglas-Rachford; feasibility; projection algorithms; iterative methods; discrete dynamical systems
- Identifier
- http://hdl.handle.net/1959.13/1399087
- Identifier
- uon:34529
- Identifier
- ISSN:1877-0533
- Rights
- This is a post-peer-review, pre-copyedit version of an article published in et-Valued and Variational Analysis. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11228-017-0457-0
- Language
- eng
- Full Text
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