A parallel row projection solver for large sparse linear systems

In this paper we present a parallel iterative solver for large and sparse nonsymmetric linear systems. The solver is based on a row-projection algorithm, derived from the symmetrized block version of the Kacz-marz method with Conjugate Gradient acceleration. A comparison with some h'rylov subspace methods shows the remarkable robustness of this algorithm when applied to systems with eingevalues arbitrarily distributed in the complex plane. Th.e parallel version of the algorithm was developed for MIMD distributed memory m.achines and it is based on a row partitioning approach which allows to compute each iteration as a simultaneous set of independent least squares problems. Moreover, we propose a data distribution strategy leading to a scalable communication scheme. The algorithm has been tested both on a system Intel iPSC/SSO and on the Intel Touchstone DELTA System, running the Intel N X message passing environment.