Parallel WZ factorization on mesh multiprocessors

Abstract

We present a parallel algorithm for the QIF (Quadrant Interlocking Factorization) method, which solves linear equation system using WZ factorization. The parallel algorithm we developed is general in the sense that it does not impose any restrictions on the size of the problem and that it is independent from the dimensions of the mesh. The result is an efficient algorithm using half the messages of the equivalent parallel LU algorithm. Finally, we have compared the QIF algorithm in multiprocessor architectures with mesh topology and hypercube topology, obtaining similar calculation times for both architectures. This last aspect confirms the communication redundancy of the hypercube topology, which raises hardware costs without any significant improvement in the efficiency of the algorithms.