BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-90-01
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Line iterative methods for cyclically reduced discrete
               convection-diffusion problems
        TYPE:: Manuscript
      AUTHOR:: Elman, Howard C.
      AUTHOR:: Golub, Gene H.
        DATE:: February 1990
       PAGES:: 34
    ABSTRACT:: We perform an analytic and empirical study of line iterative
               methods for solving the discrete convection-diffusion
               equation. The methodology consists of performing one step of
               the cyclic reduction method, followed by iteration on the
               resulting reduced system using line orderings of the reduced
               grid. Two classes of iterative methods are considered: block
               stationary methods, such as the block Gauss-Seidel and SOR
               methods, and preconditioned generalized minimum residual
               methods with incomplete LU preconditioners. New analysis
               extends convergence bounds for constant coefficient problems
               to problems with separable variable coefficients. In
               addition, analytic results show that iterative methods based
               on incomplete LU preconditioners have faster convergence
               rates than block Jacobi relaxation methods. Numerical
               experiments examine additional properties of the two classes
               of methods, including the effects of direction of flow,
               discretization, and grid ordering on performance.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-90-01