An Implementation of Parallel Eigenvalue Computation Using Dual-Level Hybrid Parallelism

  • Yonghua Zhao
  • Xuebin Chi
  • Qiang Cheng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4494)


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.


MPI/OpenMP hybrid parallel algorithm parallel solver matrix eigenvalue 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yonghua Zhao
    • 1
    • 2
    • 3
  • Xuebin Chi
    • 1
  • Qiang Cheng
    • 1
  1. 1.Supercomputing Center, Computer Network Information Center, Chinese Academy of Sciences, 100080, BeijingChina
  2. 2.Institute of Software, Chinese Academy of Sciences, 100080, BeijingChina
  3. 3.Department of Computer Science, Dezhou University, 253000, DezhouChina

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