An Exact Parallel Dense Gauss-Seidel Algorithm with Trade-Offs between Parallel Execution Time and Preprocessing Time

Abstract

The Gauss-Seidel iterative method is commonly used for solving systems of linear equations because of its good convergence properties. However, the Gauss-Seidel algorithm cannot be easily parallelized because of the data dependencies existing at each iteration. The best parallel execution time for dense systems of equations is $O(n)$ given that enough processors are available and no preprocessing is performed. In this paper we propose a new parallel Gauss-Seidel algorithm which is capable of achieving better parallel runtimes at the expense of more preprocessing time. The algorithm can be tuned in order to provide convenient trade-offs between the preprocessing time and the best parallel runtime achievable by the algorithm.