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An Efficient Parallel Algorithm for the Symmetric Tridiagonal Eigenvalue Problem

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Vector and Parallel Processing — VECPAR 2000 (VECPAR 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1981))

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Abstract

An efficient parallel algorithm, which we dubbed farm- zeroinNR, for the eigenvalue problem of a symmetric tridiagonal matrix has been implemented in a distributed memory multiprocessor with 112 nodes [1]. The basis of our parallel implementation is an improved version of the zeroinNR method [2]. It is consistently faster than simple bisection and produces more accurate eigenvalues than the QR method. As it happens with bisection, zeroinNR exhibits great flexibility and allows the computation of a subset of the spectrum with some prescribed accuracy. Results were carried out with matrices of different types and sizes up to 104 and show that our algorithm is efficient and scalable.

Available as LAPACK routine sstevd; a good choice if we desire all eigenvalues and eigenvectors of a tridiagonal matrix whose dimension is larger than about 25 [4, pg. 217].

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Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidade do Minho Campus de Gualtar, 4710-057, Braga, Portugal

    Maria Antónia Forjaz & Rui Ralha

Authors
  1. Maria Antónia Forjaz
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  2. Rui Ralha
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Editor information

Editors and Affiliations

  1. Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    José M. L. M. Palma

  2. Department of Computer Science, University of Tennessee, 37996-1301, Knoxville, TN, USA

    Jack Dongarra

  3. Departamento de Sistemas Informáticos y Computación, Universidad Politécnica de Valencia, Camino de Vera, s/n, Apartado 22012, E-46020, Valencia, Spain

    Vicente Hernández

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Forjaz, M.A., Ralha, R. (2001). An Efficient Parallel Algorithm for the Symmetric Tridiagonal Eigenvalue Problem. In: Palma, J.M.L.M., Dongarra, J., Hernández, V. (eds) Vector and Parallel Processing — VECPAR 2000. VECPAR 2000. Lecture Notes in Computer Science, vol 1981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44942-6_30

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  • DOI: https://doi.org/10.1007/3-540-44942-6_30

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  • Print ISBN: 978-3-540-41999-0

  • Online ISBN: 978-3-540-44942-3

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