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.