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.
This work is supported by the Chinese Hitech Program (863) “Supercomputing Grid Node Construction” (2002aa104540), and the
Informatization Construction of Knowledge Innovation Project of the Chinese Academy of Sciences “Supercomputing Environment
construction and Applications” (INF105-SCE).