The impact of panel factorization on the Gauss-Huard algorithm for the solution of linear systems on modern architectures

Abstract

The Gauss-Huard algorithm (the GHA) is a specialized version of Gauss-Jordan elimination for the solution of linear systems that, enhanced with column pivoting, exhibits numerical stability and computational cost close to those of the conventional solver based on the LU factorization with row pivoting. Furthermore, the GHA can be formulated as a procedure rich in matrix multiplications, so that high performance can be expected on current architectures with multi-layered memories. Unfortunately, in principle the GHA does not admit the introduction of look-ahead, a technique that has been demonstrated to be rather useful to improve the performance of the LU factorization on multi-threaded platforms with high levels of hardware concurrency. In this paper we analyze the effect of this drawback on the implementation of the GHA on systems accelerated with graphics processing units (GPUs), exposing the roles of the CPU-to-GPU and single precision-to-double precision performance ratios, as well as the contribution from the operations in the algorithm’s critical path.