Some Parallel and Vector Implementations of Preconditioned Iterative Methods on Cray-2

Parallel and vector processing algorithms of Preconditioned Iterative methods for solving sparse linear systems have been studied for the efficient use of multivector computers. Several 3D orderings, satisfying the properties of compatibility and partial compatibility [6], are introduced and implemented, using the Nested Dissection technique [11]. These preconditioners, as well as the Tridiagonal Factorization preconditioner [5], are realized on the Cray-2 using the microtasking facility. Results of numerical experiments are described to characterize these algorithms on the Cray-2.