GENERALIZED SUBSPACE CORRECTION METHODS


                                  Petter Kolm
                   Computational Mathematics and Mechanics, 
                        Royal Institute of Technology, 
                          S-100 44 Stockholm, Sweden 
                               kolm@nada.kth.se

                                 Peter Arbenz
                  Institut f\"ur Wissenschaftliches Rechnen, 
                   Eidgen\"ossische Technische Hochschule, 
                         CH-8092 Z\"urich, Switzerland
                              arbenz@inf.ethz.ch

                                 Walter Gander
                  Institut f\"ur Wissenschaftliches Rechnen, 
                   Eidgen\"ossische Technische Hochschule, 
                         CH-8092 Z\"urich, Switzerland
                              gander@inf.ethz.ch


Iterative methods for the solution of linear systems on parallel computer
architectures are presented.  Two fundamentally different iteration schemes
evolve from the theory of subspace correction:  the {\em generalized parallel
subspace correction} (*PSC) and the {\em generalized successive subspace
correction} (*SSC).  The natural parallelism of the *PSC is used to construct
several overlapping block stationary iterative methods.  Convergence is proved
for a class of these algorithms.  Numerical experiments on a 96 node Intel
Paragon XP/S5+ show that these methods have potential as scalable
preconditioners on distributed memory systems.