Efficient Implementation of CG and CR Methods for Linear Systems on a Single Processing Node of the HITACHI SR8000

We discuss the iterative methods for linear systems on a single processing node of the HITACHI SR8000. Each processing node of the SR8000 is a shared memory parallel computer which is composed of eight RISC processors with a pseudo-vector facility. We implement highly optimized codes for basic linear operations including a matrix-vector product and apply them to the conjugate gradient (CG) and the conjugate residual (CR) methods for linear systems. Our tuned codes for both method score nearly 50% of the theoretical peak performance, which is the best in the sense that it corresponds to an asymptotic performance of the inner product.