Elsevier

Parallel Computing

Volume 13, Issue 2, February 1990, Pages 199-209
Parallel Computing

Finding eigenvalues and eigenvectors of unsymmetric matrices using a distributed-memory multiprocessor

https://doi.org/10.1016/0167-8191(90)90147-2Get rights and content

Abstract

Distrubuted-memory parallel algorithms for finding the eigenvalues and eigenvectors of a dense unsymmetric matrix are given. While several parallel algorithms have been developed for symmetric matrices, little work has been done on the unsymmetric case. Our parallel implementation proceeds in three major steps: reduction of the original matrix to Hessenberg form, application of the implicit double-shift QR algoritm to compute the eigenvalues, and back transformations to compute the eigenvectors. Several modifications to our parallel QR algorithm, including ring communication, pipelining and delayed updating are discussed and compared. Results and timings are given.

References (12)

  • C.H Romine et al.

    Parallel solution of triangular systems of equations

    Parallel Comput.

    (1988)
  • D Boley et al.

    A parallel QR algorithm for the nonsymmetric eigenvalue problem

  • J.J.M Cuppen

    A divide and conquer method for the symmetric tridiagonal eigenproblem

    Numer. Math.

    (1981)
  • J.J Dongarra et al.

    A fully parallel algorithm for the symmetric eigenvalue problem

    SIAM J. Sci. Statist. Comput.

    (1987)
  • J.G.F Francis

    The QR transformation-Part 2

    Comput. J.

    (1961)
  • G.A Geist et al.

    LU factorization algorithms on distributed-memory multiprocessor architectures

    SIAM J. Sci. Statist. Comput.

    (1988)
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Research was supported by the Applied Mathematical Sciences Research Program of the Office of Energy Research, U.S. Department of Energy.

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