Abstract
This paper describes a hybrid two-level parallel method with MPI/OpenMP for computing the eigenvalues of dense symmetric matrices on cluster of SMP’s environments. The eigenvalue computation is Based on both the Householder tridiagonalization method and a divide-and-conquer algorithm of tridiagonal eigenproblem. In hybrid parallel design, We take a coarse-grain approach to OpenMP shared-memory parallelization, which keeps BLAS-3 operations in tridiagonalization. Moreover, dynamic work sharing is used in the divide-and-conquer algorithm of tridiagonal eigenproblem. So the amount of synchronization has also been reduced, and these could have an effect on the load balance. In addition, we analyze the communication overhead between hybrid MPI/ OpenMP and pure MPI. An experimental analysis on the Deepcomp6800 shows the hybrid algorithm performs good scalability.
This work was partially supported by the National Natural Science Foundation of China (No.60533020, No.60373060, No.60673064), 973 Program(2005CB321702).
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Zhao, Y., Chi, X., Cheng, Q. (2007). An Implementation of Parallel Eigenvalue Computation Using Dual-Level Hybrid Parallelism. In: Jin, H., Rana, O.F., Pan, Y., Prasanna, V.K. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2007. Lecture Notes in Computer Science, vol 4494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72905-1_10
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