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. ElmanAffiliated withDepartment of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA
  • , Gene H. GolubAffiliated withDepartment of Computer Science, Stanford University, Stanford, CA 94305, USA
  • , Gerhard StarkeAffiliated withInstitut f\"{u}r Praktische Mathematik, Universit\"{a}t Karlsruhe, Englerstrasse 2, D-76128 Karlsruhe, Germany

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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