Parallel algorithms for the solution of certain large sparse linear systems

Abstract

A couple of approximate inversion techniques are presented which provide a parallel enhancement to several iterative methods for solving linear systems arising from the discretization of boundary value problems. In particular, the Jacobi, Gauss‐Seidel, and successive overrelaxation methods can be improved substantially in a parallel environment by the extensions considered. A special case convergence proof is presented. The use of our approximate inverses with the preconditioned conjugate gradient method is examined and comparisons are made with some recently proposed algorithms in this area that also employ approximate inverses. The methods considered are compared under sequential and parallel hardware assumptions.