The Parallel Solution of Systems of Linear Equations using Iterative Methods on Transputer Networks

摘要

We present a study of the implementational aspects of iterative methods to solve systems of linear equations on a transputer network. Both dense and sparse systems are considered. First we discuss the implementation of a set of distributed linear algebra subroutines which are used as building blocks for implementing the iterative methods. We show that the use of loop-unrolling significantly increases the efficiency of these implementations. The effect of the sparsity of the matrices on the performance is analysed. Finally, serial and parallel implementations of a polynomial preconditioned Conjugate Gradient method are presented.