A Generalised Conjugate Residual method for the solution of non-symmetric systems of equations with multiple right-hand sides

This paper presents an iterative algorithm for solving non-symmetric systems of equations with multiple right- hand sides. The algorithm is an extension of the Generalised Conjugate Residual method (GCR) and combines the advantages of a direct solver with those of an iterative solver: it does not have to restart from scratch for every right-hand side, it tends to require less memory than a direct solver, and it can be implemented e ciently on a parallel computer. We will show that the extended GCR algorithm can be competitive with a direct solver when running on a single processor. We will also show that the algorithm performs well on a Cray T3E parallel computer. Copyright