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On the practical use of the lanczos algorithm in finite element applications to vibration and bifurcation problems

  • Section B Symmetric (A-λB)-Pencils And Applications
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Matrix Pencils

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 973))

Abstract

Vibration and bifurcation analyses of structures modeled by finite elements yield a linear eigenvalue problem, Kq = λ Bq, where K and B are symmetric matrices of large dimension in practical applications. An interative reduction of the matrix size is attained by the biorthogonal Lanczos algorithm which allows extraction of the lower eigenvalue spectrum. For solving the problem when coincident eigenvalues occur, a restart procedure is implemented so that further iterations can be performed from a new arbitrary vector, yielding thus to modifications in the interaction eigenvalue problem.

In addition, practical suggestions for the implementation of the method are made and efficiency of the proposed approach is demonstrated through several numerical examples.

Chargé de Recherche of the Belgian National Foundation of Scientific Research

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Authors
  1. E. G. Carnoy
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  2. M. Geradin
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Bo Kågström Axel Ruhe

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© 1983 Springer-Verlag

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Carnoy, E.G., Geradin, M. (1983). On the practical use of the lanczos algorithm in finite element applications to vibration and bifurcation problems. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062100

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  • DOI: https://doi.org/10.1007/BFb0062100

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11983-8

  • Online ISBN: 978-3-540-39447-1

  • eBook Packages: Springer Book Archive

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