Numerische Mathematik

, Volume 67, Issue 2, pp 177–190

On the convergence of line iterative methods for cyclically reduced non-symmetrizable linear systems

  • Howard C. Elman
  • Gene H. Golub
  • Gerhard Starke

DOI: 10.1007/s002110050023

Cite this article as:
Elman, H., Golub, G. & Starke, G. Numer. Math. (1994) 67: 177. doi:10.1007/s002110050023


We derive analytic bounds on the convergence factors associated with block relaxation methods for solving the discrete two-dimensional convection-diffusion equation. The analysis applies to the reduced systems derived when one step of block Gaussian elimination is performed on red-black ordered two-cyclic discretizations. We consider the case where centered finite difference discretization is used and one cell Reynolds number is less than one in absolute value and the other is greater than one. It is shown that line ordered relaxation exhibits very fast rates of convergence.

Mathematics Subject Classification (1991): 65F10

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Howard C. Elman
    • 1
  • Gene H. Golub
    • 2
  • Gerhard Starke
    • 3
  1. 1.Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA US
  2. 2.Department of Computer Science, Stanford University, Stanford, CA 94305, USA US
  3. 3.Institut f\"{u}r Praktische Mathematik, Universit\"{a}t Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany DE