Multi-Level Minimal Residual Smoothing: A Family of 
              General Purpose Multigrid Acceleration Techniques

                                  Jun Zhang

              jzhang@cs.uky.edu   http://www.cs.uky.edu/~jzhang

                       Department of Computer Science 
                            University of Kentucky
                              773 Anderson Hall 
                       Lexington, Kentucky 40506--0046

                                   Abstract

We employ multi-level minimal residual smoothing (MRS) as a pre-optimization
technique to accelerate standard multigrid convergence.  The MRS method is
used to improve the current multigrid iterate by smoothing its corresponding
residual before the latter is projected to the coarse grid.  We develop
different schemes for implementing MRS technique on the finest grid and on the
coarse grids, and several versions of the inexact MRS technique.  Numerical
experiments are conducted to show the efficiency of the multi-level and
inexact MRS techniques.