A parallel Krylov-type method for nonsymmetric linear systems

Abstract. Parallel Krylov (S-step and block) iterative methods for linear systems have been studied and implemented in the past. In this ar-ticle we present a parallel Krylov method based on block s-step method for nonsymmetric linear systems. We derive two new averaging algorithm to combine several approximations to the solution of a single linear sys-tem using the block method with multiple initial guesses. We implement the new methods with ILU preconditioners on a parallel computer. We test the accuracy and present performance results.