Conjugate-gradient subroutines for the IBM 3090 Vector Facility

This paper describes a set of optimized subroutines for use in solving sparse, symmetric, positive definite linear systems of equations using iterative algorithms. The set has been included in the Engineering and Scientific Subroutine Library (ESSL) for the IBM 3090 Vector Facility (VF). The subroutines are based on the conjugate-gradient method, preconditioned by the diagonal or by an incomplete factorization. They make use of storage representations of sparse matrices that are optimal for vector implementation. The ESSL vector subroutines are up to six times faster than a scalar implementation of the same algorithm.