Polyhedral Gauß-Seidel converges

Graeser C, Sander O (2014)

Publication Type: Journal article

Publication year: 2014

Journal

Journal of Numerical Mathematics Walter de Gruyter

Book Volume: 22

Pages Range: 221-254

Journal Issue: 3

DOI: 10.1515/jnma-2014-0010

Abstract

We prove global convergence of an inexact extended polyhedral Gauß-Seidel method for the minimization of strictly convex functionals that are continuously differentiable on each polyhedron of a polyhedral decomposition of their domains of definition. While pure Gauß-Seidel methods are known to be very slow for problems governed by partial differential equations, the presented convergence result also covers multilevel methods that extend the Gauß-Seidel step by coarse level corrections. Our result generalizes the proof of [10] for differentiable functionals on the Gibbs simplex. Example applications are given that require the generality of our approach.

Authors with CRIS profile

Carsten Gräser

Involved external institutions

Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen DE Germany (DE) Freie Universität Berlin DE Germany (DE)

How to cite

APA:

Graeser, C., & Sander, O. (2014). Polyhedral Gauß-Seidel converges. Journal of Numerical Mathematics, 22(3), 221-254. https://dx.doi.org/10.1515/jnma-2014-0010

MLA:

Graeser, C., and O. Sander. "Polyhedral Gauß-Seidel converges." Journal of Numerical Mathematics 22.3 (2014): 221-254.

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