Skip to main content
SpringerLink
Log in

TheQ R algorithm for real hessenberg 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

Log in via an institution

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

Instant access to the full article PDF.

References

  1. Francis, J. C. F.: TheQ R transformation — a unitary analogue to theLR transformation. Computer journal4, 265–271 and 332-345 (1961/62).

    Google Scholar 

  2. Householder, A. S.: Unitary triangularization of a non-symmetric matrix. J. Assoc. Comp. Mach.5, 339–342 (1958).

    Google Scholar 

  3. —— Bauer, F. L.: On certain methods for expanding the characteristic polynomial. Numerische Math.1, 29–37 (1959)

    Google Scholar 

  4. Kublanovskaya, V. N.: On some algorithms for the solution of the complete eigenvalue problem. Zh. Vych. Mat.1, 555–570 (1961).

    Google Scholar 

  5. Martin, R. S., Wilkinson, J. H.: Similarity reduction of a general matrix to Hessenberg form. Numerische Math.12, 349–368 (1968).

    Google Scholar 

  6. Parlett, B. N.: Global convergence of the basicQR algorithm on Hessenberg matrices. Math. of Computation22, 803–817 (1968).

    Google Scholar 

  7. —— Reinsch, C.: Balancing a matrix for calculation of eigenvalues and eigenvectors. Numerische Math.13, 293–304 (1969)

    Google Scholar 

  8. Wilkinson, J. H.: The algebraic eigenvalue problem. London: Oxford University Press 1965.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Physical Laboratory, Teddington, Middlesex, Great Britain

    J. H. Wilkinson

Authors
  1. R. S. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Peters
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. H. Wilkinson
    View author publications

    You can also search for this author in PubMed Google Scholar

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 in ALGOL 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

Martin, R.S., Peters, G. & Wilkinson, J.H. TheQ R algorithm for real hessenberg matrices. Numer. Math. 14, 219–231 (1970). https://doi.org/10.1007/BF02163331

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02163331

Keywords

Search

Navigation