Abstract

. We show how highly efficient parallel implementations of basic linear algebra routines may be used as building blocks to implement efficient higher level algorithms. We discuss the solution of systems of linear equations using a preconditioned Conjugate-Gradients iterative method on a network of transputers. Results are presented for the solution of both dense and sparse systems; the latter being derived from the finite-difference approximation of partial differential equations. 1 Introduction The numerical solution of non-singular systems of N linear equations, Ax = b (1) is required in a wide range of practical applications. When N is large, the solution of (1) becomes time-consuming and techniques must be sought to accelerate the solution process. This may be accomplished by 1. using an iterative method with an improved rate of convergence, possibly with the aid of preconditioning, 2. devising a parallel implementation of the method that allows the efficient use of a parallel m...

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