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Numerische Mathematik

, Volume 9, Issue 1, pp 1–10 | Cite as

The Jacobi method for real symmetric matrices

  • H. Rutishauser
Handbook Series Linear Algebra

Keywords

Mathematical Method Symmetric Matrice 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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    Barth, W., andJ. H. Wilkinson: The bisection method. Numer. Math. (to appear).Google Scholar
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    Gregory, R. T.: Computing eigenvalues and eigenvectors of a symmetric matrix on the ILLIAC. Math. Tab. and other Aids to Comp.7, 215–220 (1953)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. Soc. Ind. Appl. Math.6, 144–162 (1958)Google Scholar
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    Jacobi, C. G. J.: Über ein leichtes Verfahren, die in der Theorie der Säkularstörungen vorkommenden Gleichungen numerisch aufzulösen. Crelle's Journal30, 51–94 (1846).Google Scholar
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    Pope, D. A., andC. Tompkins: Maximizing functions of rotations-experiments concerning speed of diagonalisation of symmetric matrices using Jacobi's method. J. Ass. Comp. Mach.4, 459–466 (1957).Google Scholar
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    Rutishauser, H., andH. R. Schwarz: The LR-transformation method for symmetric matrices. Numer. Math.5, 273–289 (1963).Google Scholar
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    Schoenhage, A.: Zur Konvergenz des Jacobi-Verfahrens. Num. 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
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    —— Householder's method for symmetric matrices. Numer. Math.4, 354–361 (1962).Google Scholar
  10. [10]
    —— Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection. Numer. Math.4, 362–367 (1962).Google Scholar
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    —— Calculation of the eigenvectors of a symmetric tridiagonal matrix by inverse iteration. Numer. Math.4, 368–372 (1962).Google Scholar
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    —— The algebraic eigenvalue problem, 662 p. Oxford: Clarendon Press 1965Google Scholar

Copyright information

© Springer-Verlag 1966

Authors and Affiliations

  • H. Rutishauser
    • 1
  1. 1.Technische HochschuleInstitut für Angewandte Mathematik EidgenZürich/Schweiz

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