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Numerische Mathematik

, Volume 9, Issue 1, pp 11–18 | Cite as

On the convergence of the classical Jacobi method for real symmetric matrices with non-distinct eigenvalues

  • H. P. M. van Kempen
Article

Summary

It is proved that the classical Jacobi method for real symmetric matrices with multiple eigenvalues converges quadratically.

Keywords

Mathematical Method Symmetric Matrice Multiple Eigenvalue Jacobi Method Real Symmetric Matrice 
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

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    Forsythe, G. E., andP. Henrici: The cyclic Jacobi method. Trans. Amer. Math. Soc.94, 1–23 (1960).Google Scholar
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    Goldstine, H. H., F. J. Murray, andJ. von Neumann: The Jacobi method for real symmetric matrices. J.A.C.M.6, 59–96 (1959)Google Scholar
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    Hansen, E. R.: On quasicyclic Jacobi methods. J.A.C.M.9, 118–135 (1962).Google Scholar
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    Henrici, P.: On the speed of convergence of cyclic and quasicyclic Jacobi methods for computing eigenvalues of Hermitian matrices. J.S.I.A.M.6, 144–62 (1958)Google Scholar
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    Pope, D. E., andC. Tompkins: Maximizing functions of rotations. J.A.C.M.4, 459–466 (1957)Google Scholar
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    Schönhage, A.: Zur Konvergenz des Jacobi-Verfahrens. Numer. Math.3, 374–380 (1961).Google Scholar
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    Wilkinson, J. H.: Note on the quadratic convergence of the cyclic Jacobi process. Numer. Math.4, 296–300 (1962).Google Scholar

Copyright information

© Springer-Verlag 1966

Authors and Affiliations

  • H. P. M. van Kempen
    • 1
  1. 1.Koninklijke/Shell-LaboratoriumAmsterdam-N (Holland)

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