Parallel Linear Algebra on Clusters

Parallel performance optimization is being applied and further improvements are studied for parallel linear algebra on clusters. Several parallelization guidelines have been defined and are being used on single clusters and local area networks used for parallel computing. In this context, some linear algebra parallel algorithms have been implemented following the parallelization guidelines, and experimentation has shown very good performance. Also, the parallel algorithms outperform the corresponding parallel algorithms implemented on ScaLAPACK (Scalable LAPACK), which is considered to have highly optimized parallel algorithms for distributed memory parallel computers. Also, using more than a single cluster or local area network for parallel linear algebra computing seems to be a natural approach, taking into account the high availability of such computing platforms in academic/research environments. In this context of multiple clusters, there are many interesting challenges, and many of them are still to be exactly defined and/or characterized. Intercluster communication performance characterization seems to be the first factor to be precisely quantified and it is expected that communication performance quantification will give a starting point from which analyze current and future approaches for parallel performance using more than one cluster or local area network for parallel cooperating processing.