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On bounds for symmetric eigenvalue problems

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

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

Abstract

Bounds for the eigenvalues of Ax = λBx are derived where A and B are symmetric and B is also positive definite with a matrix factor G such that B = GTG. The method depends on it being possible to obtain a lower bound for the singular values of G by a method recently developed by the author.

Keywords

  • Eigenvalue Problem
  • Civil Engineer Department
  • Algebraic Eigenvalue Problem
  • Symmetric Eigenvalue Problem
  • Hinge Rotation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. ALAN JENNINGS, Bounds for the singular values of a matrix, IMAJNA, to be published.

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  2. A.S. HOUSEHOLDER, The Theory of Matrices in Numerical Analysis, Dover, New York, 1964.

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  3. J.H. WILKINSON, The Algebraic Eigenvalue Problem, Oxford, Clarendon Press, 1965.

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  4. ALAN JENNINGS, Matrix Computation for Engineering and Scientists, Wiley, London, 1977.

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  5. H.G. ALLEN, and P.S. BULSON, Background to Buckling, McGraw-Hill, London, 1980.

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© 1983 Springer-Verlag

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Jennings, A. (1983). On bounds for symmetric eigenvalue problems. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062103

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  • DOI: https://doi.org/10.1007/BFb0062103

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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