Dynamics of the Douglas-Rachford Method for Ellipses and p-Spheres
| Autor: | Anna Schneider, Matthew P. Skerritt, Brailey Sims, Jonathan M. Borwein, Scott B. Lindstrom |
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| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Numerical Analysis 021103 operations research Applied Mathematics 0211 other engineering and technologies Order (ring theory) 010103 numerical & computational mathematics 02 engineering and technology Ellipse 01 natural sciences Functional Analysis (math.FA) Local convergence Mathematics - Functional Analysis Iterated function Dynamics (music) Convergence (routing) Line (geometry) FOS: Mathematics 47H99 49M30 65Q30 90C26 Applied mathematics SPHERES Geometry and Topology 0101 mathematics Analysis Mathematics |
| Zdroj: | Set-Valued and Variational Analysis. 26:385-403 |
| ISSN: | 1877-0541 1877-0533 |
| DOI: | 10.1007/s11228-017-0457-0 |
| Popis: | 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 $p$-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. |
| Databáze: | OpenAIRE |
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