Parallel gaussian elimination of symmetric positive definite band matrices for shared-memory multicore architectures

Abstract

This study presents a new parallel Gaussian elimination approach for symmetric positive definite band systems. For each task, the appropriate start time and adequate processor are determined. Unnecessary dependencies between tasks are eliminated. Simultaneously, all processors perform their associated tasks with precedence constraints under consideration. Our main goal is to obtain a high degree of parallelism by balancing the load of processors and reducing the total idle and parallel execution times. The theoretical lower bounds for parallel execution time and number of processors required to execute the precedence graph at an optimal time are also computed. The validity of our investigation is confirmed by carrying out several experiments on a shared-memory multicore architecture using OpenMP. Practical results prove the efficiency of the proposed method.