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Preconditioned iterative methods for the generalized eigenvalue problem

  • 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))

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Abstract

In this paper a preconditioned iterative method suitable for the solution of the generalized eigenvalue problem is presented. The proposed method is suitable for the determination of the extreme eigenvalues and their corresponding eigenvectors of the large sparse matrices derived from finite element/difference discretisation of partial differential equations. The new strategy when coupled with the conjugate gradient algorithm yields a powerful method for this class of problems.

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References

  1. D.J. EVANS, The use of preconditioning in iterative methods for solving linear equations with symmetric positive definite matrices, J.Inst.Math.Applics., 4 (1968), pp.295–314.

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  3. D.J. EVANS AND J. SHANEHCHI, Preconditioned iterative methods for the large sparse symmetric eigenvalue problem, Comp.Meth.Appl.Mech. & Eng. (1982), in press.

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  4. M.R. HESTENES AND E. STIEFEL, Methods of conjugate gradients for solving linear systems, Jour. of Res., N.B.S., 49 (1952), pp.409–436.

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  5. A. RUHE, SOR methods for the eigenvalue problem with large sparse matrices, Math. of Comp. 28 (1974), pp.697–710.

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  7. A. RUHE AND T. WIBERG, The method of conjugate gradients used in inverse iteration, B.I.T. 12 (1972), pp.543–554.

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Authors
  1. D. J. Evans
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Bo Kågström Axel Ruhe

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© 1983 Springer-Verlag

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Evans, D.J. (1983). Preconditioned iterative methods for the generalized eigenvalue problem. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062102

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  • DOI: https://doi.org/10.1007/BFb0062102

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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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