Accelerating Gauss-Huard Using LU-Based Panel Factorization on Hybrid Machinery

In our prior work, we addressed a bottleneck in the Gauss-Huard algorithm at the panel factorization step, which had been identified as a challenge in the existing research. We introduced the look-ahead technique using the delayed Gauss-Huard algorithm and random butterfly transformations to tackle this issue. However, as noted in the literature and confirmed by our findings, the performance of the delayed approach was inferior to that of LU factorization. In this extended study, we propose a transition to LU factorization for the panel factorization step, retaining the use of the look-ahead technique, and thereby significantly enhancing the Gauss-Huard algorithm’s efficiency. Validation involved a performance comparison with Gaussian elimination in the MAGMA library, and accuracy and stability testing across 21 diverse test matrices. The Gauss-Huard algorithm with LU factorization significantly outperformed Gaussian elimination in hybrid computing environments, achieving a speedup of 3.24x. Moreover, the accuracy and stability were consistently within acceptable error bounds. These results show that the integration of LU factorization with the Gauss-Huard algorithm not only overcomes the deficiencies of the delayed approach but also realizes the combined strengths of both methodologies.