Skip to main content
Log in

The Jacobi method for real symmetric matrices

  • Handbook Series Linear Algebra
  • Published:
Numerische Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Barth, W., andJ. H. Wilkinson: The bisection method. Numer. Math. (to appear).

  2. 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 

  3. 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 

  4. 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 

  5. 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 

  6. Rutishauser, H., andH. R. Schwarz: The LR-transformation method for symmetric matrices. Numer. Math.5, 273–289 (1963).

    Google Scholar 

  7. Schoenhage, A.: Zur Konvergenz des Jacobi-Verfahrens. Num. Math.3, 374–380 (1961).

    Google Scholar 

  8. Wilkinson, J. H.: Note on the quadratic convergence of the cyclic Jacobi process. Numer. Math.4, 296–300 (1962).

    Google Scholar 

  9. —— Householder's method for symmetric matrices. Numer. Math.4, 354–361 (1962).

    Google Scholar 

  10. —— Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection. Numer. Math.4, 362–367 (1962).

    Google Scholar 

  11. —— Calculation of the eigenvectors of a symmetric tridiagonal matrix by inverse iteration. Numer. Math.4, 368–372 (1962).

    Google Scholar 

  12. —— The algebraic eigenvalue problem, 662 p. Oxford: Clarendon Press 1965

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Editor's note.In this fascicle, prepublication of algorithms from the Linear Algebra series of the Handbook for Automatic Computation is continued. Algorithms are published inAlgol 60 reference language as approved by the IFIP. Contributions in this series should be styled after the most recently published ones.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rutishauser, H. The Jacobi method for real symmetric matrices. Numer. Math. 9, 1–10 (1966). https://doi.org/10.1007/BF02165223

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02165223

Keywords

Navigation