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Some Unusual Eigenvalue Problems

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Vector and Parallel Processing – VECPAR’98 (VECPAR 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1573))

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Abstract

We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the well-known Gauss-type quadrature rules and Lanczos process are reviewed for computing these quadratic forms. These algorithms reference the matrix in question only through a matrix-vector product operation. Hence it is well suited for large sparse problems. Some selected numerical examples are presented to illustrate the efficiency of such an approach.

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Author information

Authors and Affiliations

  1. University of Kentucky, Lexington, KY, 40506, USA

    Zhaojun Bai

  2. Stanford University, Stanford, CA, 94305, USA

    Gene H. Golub

Authors
  1. Zhaojun Bai
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  2. Gene H. Golub
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Editor information

Editors and Affiliations

  1. EUIT Telecomunicación - DIATEL, Universidad Politécnica de Madrid, Ctra., Valencia, Km. 7, 28031, Madrid, Spain

    Vicente Hernández

  2. Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n, 4200-465, Porto, Portugal

    José M. L. M. Palma

  3. Computer Science Department, University of Tennessee, TN 37996-3450, Knoxville, USA

    Jack J. Dongarra

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© 1999 Springer-Verlag Berlin Heidelberg

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Bai, Z., Golub, G.H. (1999). Some Unusual Eigenvalue Problems. In: Hernández, V., Palma, J.M.L.M., Dongarra, J.J. (eds) Vector and Parallel Processing – VECPAR’98. VECPAR 1998. Lecture Notes in Computer Science, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703040_2

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  • DOI: https://doi.org/10.1007/10703040_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66228-0

  • Online ISBN: 978-3-540-48516-2

  • eBook Packages: Springer Book Archive

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