An implementation of parallel eigenvalue computation using dual-level hybrid parallelism

Authors:
Yonghua Zhao;Xuebin Chi;Qiang Cheng
Affiliations:
Supercomputing Center, Computer Network Information Center, Chinese Academy of Sciences, Beijing, China and Institute of Software, Chinese Academy of Sciences, Beijing, China and Department of Com ...;Supercomputing Center, Computer Network Information Center, Chinese Academy of Sciences, Beijing, China;Supercomputing Center, Computer Network Information Center, Chinese Academy of Sciences, Beijing, China
Venue:
ICA3PP'07 Proceedings of the 7th international conference on Algorithms and architectures for parallel processing
Year:
2007

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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.