In field computation, the quick solution of sparse, symmetric and positive definite systems of equations is important. In this paper we present a parallelization of the well known Jacobi Conjugate Gradients scheme which was originally intended for memory short pc environments. We show that by storing the element matrices at some cost in storage, we possess a very fast conjugate gradients algorithm because of its simplicity and ease of parallelization. This algorithm is the compared with sequential and parallel implementations of other conjugate gradients algorithms and it is shown that although some of the others require fewer iterations, this algorithm maintains its superiority in computation time by avoiding the expensive forward elimination and back substitution operations repeatedly required by the others. For the first time, the comparisons are up to a matrix size of 11,800 × 11,800.
Mahinthakumar et al. (1990) studied this question.