BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-89-01
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Iterative methods for cyclically reduced non-self-adjoint
               linear systems
        TYPE:: Manuscript
      AUTHOR:: Elman, Howard C.
      AUTHOR:: Golub, Gene H.
        DATE:: February 1989
       PAGES:: 32
    ABSTRACT:: We study iterative methods for solving linear systems of the
               type arising from two-cyclic discretizations of
               non-self-adjoint two-dimensional elliptic partial
               differential equations. A prototype is the
               convection-diffusion equation. The methods consist of
               applying one step of cyclic reduction, resulting in a
               "reduced system" of half the order of the original discrete
               problem, combined with a reordering and a block iterative
               technique for solving the reduced system. For constant
               coefficient problems, we present analytic bounds on the
               spectral radii of the iteration matrices in terms of cell
               Reynolds numbers that show the methods to be rapidly
               convergent. In addition, we describe numerical experiments
               that supplement the analysis and that indicate that the
               methods compare favorably with methods for solving the
               "unreduced" system.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-89-01