Numerische Mathematik

, Volume 52, Issue 6, pp 701–723 | Cite as

Estimates for multigrid methods based on red-black Gauss-Seidel smoothings

  • Seymour V. Parter


TheMGR[v] algorithms of Ries, Trottenberg and Winter, the Algorithms 2.1 and 6.1 of Braess and the Algorithm 4.1 of Verfürth are all multigrid algorithms for the solution of the discrete Poisson equation (with Dirichlet boundary conditions) based on red-black Gauss-Seidel smoothing. Both Braess and Verfürth give explicit numerical upper bounds on the rate of convergence of their methods in convex polygonal domains. In this work we reconsider these problems and obtain improved estimates for theh−2h Algorithm 4.1 as well asW-cycle estimates for both schemes in non-convex polygonal domains. The proofs do not depend on the strengthened Cauchy inequality.

Subject Classifications

AMS(MOS): 65 N 20 CR: G 1.8 


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Seymour V. Parter
    • 1
  1. 1.Computer Science DepartmentUniversity of WisconsinMadisonUSA

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