Solving the Symmetric Tridiagonal Eigenproblem Using MPI/OpenMP Hybrid Parallelization

We present a hybrid MPI/OpenMP parallel implementation for the eigenvalues of symmetric tridiagonal matrices on cluster of SMP’s environments. The algorithm is based on a divide-and-conquer method which uses the split-merge technique and Laguerre’s iteration. We study two different implementations of the algorithm: one based on MPI and the other based on a hybrid parallel paradigm with MPI/OpenMP. We take a coarse grain OpenMP approach to parallel implementation for solving the eigenvalues of symmetric tridiagonal submatrices within a SMP node. And dynamic work sharing is used in Laguerre’s iterations. This has two effects: first, the amount of synchronization has been reduced; secondly, this could have an effect on the load balance. In addition, we analyze the communication overhead on two different implementations. An experimental analysis on the DeepComp 6800 shows the hybrid algorithm performs good scalability.

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