Efficient Algorithms for Matrix Eigenproblem Solver on SMP Cluster

Tridiagonalization of symmetric matrices and computing eigenvalues of tridiagonal symmetric matrix are the keys of eigenproblem parallel solver of dense symmetric matrix. Aimed at the memory hierarchy of the SMP cluster and based on both matrix tridiagonalization using Householder transform and divide-and-conquer algorithm for tridiagonal eigenproblem, their MPI+OpenMP hybrid parallel implementations are presented. These studies focus on load balance, communication overhead and performance evaluation on the SMP cluster. Hybrid parallel algorithm design combines the coarse-grain model and dynamic task sharing, thus resolving the load balance problem and decreasing the communication overhead in MPI parallel algorithm. It is shown from the tests on Deepcomp 6800 that the parallel solver based on hybrid parallel implementation has better performance and scalability than that based on pure MPI implementation.