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Hybrid algorithms for the elgensolution of large sparse symmetric matrices on the AMT DAP 510

  • M. Clint
  • J. S. Weston
  • C. W. Bleakney
Array Processors And Applications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 457)

Abstract

In this paper a method for the eigensolution of large sparse symmetric matrices with regular structures is presented. The method is applied by first extracting the diagonal submatrices of the target matrix and assembling from the matrices of their eigenvectors an approximation to the matrix of eigenvectors of the large system. The eigensolutions of the small matrices may be computed using any appropriate algorithm; indeed, the choice of algorithm may vary from submatrix to submatrix. The eigenvectors of the target system are then constructed by refining the matrix of approximate eigenvectors. The algorithm used in this refinement process may be efficiently implemented, for matrices of any size, on an array processor. In this paper experience of using the method on an AMT DAP 510 is reported, and the efficiency of its performance is favourably compared with a related method [1] for solving problems of a similar kind.

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References

  1. 1.
    J.S. Weston and M. Clint, Two algorithms for the parallel computation of eigenvalues and eigenvectors of large symmetric matrices using the ICL DAP, Parallel Computing 13 (1990) 281–288.CrossRefGoogle Scholar
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    M. Clint, C. Holt, R. Perrott and A. Stewart, A DAP Fortran subroutine for the eigensolution of real symmetric matrices, Comput. J. 28 (1985) 340–342.CrossRefGoogle Scholar
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    AMT, DAP General Support Library, (1988).Google Scholar
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    M. Clint, C. Holt, R. Perrott and A. Stewart, A comparison of two parallel algorithms for the symmetric eigenproblem, Intern. J. Comput. Math. 15 (1984) 291–302.Google Scholar
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    R.T. Gregory and D.L. Karney, A Collection of Matrices for Testing Computational Algorithms (Wiley, New York, 1969).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • M. Clint
    • 1
  • J. S. Weston
    • 2
  • C. W. Bleakney
    • 3
  1. 1.Department of Computer ScienceThe Queen's University of BelfastBelfastN. Ireland
  2. 2.Department of Computing ScienceUniversity of Ulster at ColeraineColeraineN. Ireland
  3. 3.The Computer CentreThe Queen's University of BelfastBelfastN. Ireland

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