Solving the Symmetric Tridiagonal Eigenproblem Using MPI/OpenMP Hybrid Parallelization

  • Yonghua Zhao
  • Jiang Chen
  • Xuebin Chi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3756)


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.


Tridiagonal Matrix Hybrid Program Tridiagonal Matrice Parallel Speedup Master Processor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yonghua Zhao
    • 1
    • 2
    • 3
  • Jiang Chen
    • 1
  • Xuebin Chi
    • 1
  1. 1.Supercomputing Center, Computer Network Information CenterChinese Academy of SciencesBeijingChina
  2. 2.Graduate SchoolChinese Academy of SciencesBeijingChina
  3. 3.Department of Computer ScienceDezhou UniversityShandongChina

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