Polyhedral Gauß–Seidel converges

Research output: Contribution to journalResearch articleContributedpeer-review


  • Carsten Gräser - , Free University of Berlin (Author)
  • Oliver Sander - , RWTH Aachen University (Author)


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.


Original languageEnglish
Pages (from-to)221-254
JournalJournal of Numerical Mathematics
Issue number3
Publication statusPublished - 7 Oct 2014
Externally publishedYes

External IDs

Scopus 84908085451
ORCID /0000-0003-1093-6374/work/142250583


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