Empirical Performance Evaluation of Gaussian Elimination and Parallel Implicit Elimination with Parallel Computing Technologies

Empirical performance evaluation of parallel processing methods is a means of judging the speedup and efficiency of these methods. Many factors may affect on the time of processing. Some of these factors were recently studied such as (Implicit Matrix Elimination (IME), WZ and CG) methods. Some other factors have yet to be studied such as Gaussian Elimination (GE) and Parallel Implicit Elimination (PIE) algorithms. Gaussian elimination (GE) is a method for analyzing systems of linear equations. The Parallel Implicit Elimination method (PIE) is a design that eliminates more than one element simultaneously (not one element as in GE). This paper aims to study (GE & PIE) methods and its effects on the performance of processing. Five matrices are selected and processed using four different number of Threads (T) (2, 4, 8 and 16 processors). Sequential times are computed for the processing of these matrices. The matrices are then processed using available shared and distributed memory technologies (MPI, OpenMP, and Pthread). Execution times for the parallel processing values calculated with reference to the sequential times. The speedup and efficiency values are then analyzed statistically to distinguish the impacts of these algorithms. From the results, OpenMP is found to be better (on average) compared to Pthread and MPI. For each of the four processors, Open MP and Pthread perform better than MPI. The (GE & PIE) are affected differently by the increase of Processors. In general, we found that The speedup of PIE method is better than GE method by increasing number of processors but the efficiency will be decrease gradually because the complexity at each node.