Parallel Heuristics for Systems of Equations Preconditioning

This paper proposes two parallel hybrid heuristics aiming for the reduction of the average bandwidth of sparse matrices, process used in systems of equations preconditioning. Based on a direct processing of the matrix, the first method combines a heuristic inspired from the laws of physics, with a greedy selection of rows/columns to be interchanged. The second one improves the previous heuristic through the use of an exact formula for determining the most favorable interchanges. Experimental results obtained on an IBM Blue Gene /P supercomputer illustrate the fact that the proposed parallel heuristics lead to better results, with respect to time efficiency, speedup, efficiency and solution.