A parallelizable and fast algorithm for very large generalized eigenproblems | SpringerLink
Skip to main content
Springer Nature Link
Log in

A parallelizable and fast algorithm for very large generalized eigenproblems

  • Conference paper
  • First Online:
Applied Parallel Computing Industrial Computation and Optimization (PARA 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1184))

Included in the following conference series:

Abstract

We discuss a novel iterative approach for the computation of a number of eigenvalues and eigenvectors of the generalized eigenproblem Ax=λBx. Our method is based on a combination of the Jacobi-Davidson method and the QZ-method. For that reason we refer to the method as JDQZ. The effectiveness of the method is illustrated by a numerical example.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. W. E. Arnoldi. The principle of minimized iteration in the solution of the matrix eigenproblem. Quart. Appl. Math., 9:17–29, 1951.

    Google Scholar 

  2. J.G.L. Booten, D.R. Fokkema, G.L.G. Sleijpen, and H.A. van der Vorst. Jacobi-Davidson methods for generalized MHD-eigenvalue problems. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 1996.

    Google Scholar 

  3. J. Cullum, W. Kerner, and R. Willoughby. A generalized nonsymmetric Lanczos procedure. Computer Physics Communications, 53:19–48, 1989.

    Google Scholar 

  4. D.R. Fokkema, G.L.G. Sleijpen, and H.A. van der Vorst. Jacobi-Davidson style QR and QZ algorithms for the partial reduction of matrix pencils. Technical Report Preprint 941, Mathematical Institute, Utrecht University, 1996.

    Google Scholar 

  5. G. H. Golub and C. F. van Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore, 1989.

    Google Scholar 

  6. G. L. G. Sleijpen and H.A. Van der Vorst. A Jacobi-Davidson iteration method for linear eigenvalue problems. SIAM J. Matrix Anal.Appl., 17(2):401–425, 1996.

    Google Scholar 

  7. D. C. Sorenson. Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matr. Anal. Appl., 13(1):357–385, 1992.

    Google Scholar 

  8. M.B. Van Gijzen. A parallel eigensolution of an acoustic problem with damping, submitted for publication.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, University of Utrecht, Budapestlaan 6, Utrecht, the Netherlands

    Henk A. van der Vorst & Gerard L. G. Sleijpen

Authors
  1. Henk A. van der Vorst
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerard L. G. Sleijpen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Jerzy Waśniewski Jack Dongarra Kaj Madsen Dorte Olesen

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van der Vorst, H.A., Sleijpen, G.L.G. (1996). A parallelizable and fast algorithm for very large generalized eigenproblems. In: Waśniewski, J., Dongarra, J., Madsen, K., Olesen, D. (eds) Applied Parallel Computing Industrial Computation and Optimization. PARA 1996. Lecture Notes in Computer Science, vol 1184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62095-8_74

Download citation

  • DOI: https://doi.org/10.1007/3-540-62095-8_74

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62095-2

  • Online ISBN: 978-3-540-49643-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation