Multigrid with Inexact 
         Minimal Residual Smoothing Acceleration

                         Jun Zhang

                 Department of Mathematics
             The George Washington University 
                    Washington, DC 20052

                       March 5, 1996

(For a hard copy, send an e-mail to: zhang@math.gwu.edu.)

                          Abstract

We introduce some inexact versions of the minimal residual smoothing (IMRS)
technique to accelerate the standard multigrid convergence.  These are
modified versions of the minimal residual smoothing (MRS) technique introduced
and analyzed in earlier papers.  The IMRS acceleration schemes reduce the cost
of the standard MRS acceleration by about 40% for two dimensional problems and
frequently achieve even faster convergence.  Numerical experiments are
employed to demonstrate the efficiency of the IMRS acceleration schemes.  Some
of the numerical results show that IMRS can reduce the numbers of iterations
by 88% with respect to the standard multigrid method.