Revisiting the Gauss-Huard Algorithm for the Solution of Linear Systems on Graphics Accelerators

Abstract

In 1979, P. Huard presented an efficient variant of the Gauss-Jordan elimination for the solution of linear systems. In particular, this alternative algorithm exhibits the same computational cost as the traditional LU-based solver, and is considerably cheaper than the Gauss-Jordan algorithm, but there exist no recent high performance implementations of the Gauss-Huard (GH) variant that allow a comparison of these approaches. In this paper we present a reliable GH solver for hybrid platforms equipped with conventional multi-core technology and a graphics processing unit (GPU). The experimental results show that the GH algorithm can beat high performance versions of the LU solver, from tuned libraries for CPU-GPU servers such as MAGMA, for problems of small to moderate scale.