Clustered Gauss–Huard algorithm for the solution of Ax = b

Abstract

In this paper, we present and evaluate a new parallel algorithm for Gauss–Huard method with scaled partial pivoting strategy for the solution of linear systems of equations. The algorithm is generic in the sense that matrix distribution methods are decoupled from the algorithm details which makes it applicable to a wide spectrum of distribution functions and hence saving the additional efforts that would be needed to develop a new algorithm for every instance of matrix distribution functions. The proposed algorithm is first analyzed then evaluated using a cluster of networked workstations. A timing model is developed and verified to accurately estimate the execution time of the proposed algorithm. The obtained results reveal two important observations: First, cluster computing is a viable and low-cost alternative for solving computationally intensive problems such as achieving fast and stable solutions for systems of linear equations; a problem often encountered in many real-life applications. Second, the obtained results reveal that Gauss–Huard performs better than the well known Gauss–Jordan algorithm in cluster environments.