Householder’s Tridiagonalization of a Symmetric Matrix

  • R. S. Martin
  • C. Reinsch
  • J. H. Wilkinson
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)


In an early paper in this series [4] Householder’s algorithm for the tridiagonalization of a real symmetric matrix was discussed. In the light of experience gained since its publication and in view of its importance it seems worthwhile to issue improved versions of the procedure given there. More than one variant is given since the most efficient form of the procedure depends on the method used to solve the eigenproblem of the derived tridiagonal matrix.


Linear Array Tridiagonal Matrix Binary Digit Inverse Iteration Lower Triangle 
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  1. 1.
    Barth, W., R. S. Martin, and J. H. Wilkinson : Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection. Numer. Math. 9, 386–393 (1967). Cf. II/5.MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bowdler, H., R. S. Martin, C. Reinsch, and J. H. Wilkinson. The QR and QL algorithms for symmetric matrices. Numer. Math. 11, 293 -306 (1968). Cf. II/3.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Ortega, J. M.: An error analysis of Householder’. method for the symmetric eigenvalue problem. Numer. Math. 5, 211–225 (1963).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Wilkinson, J. H.: Householder’. method for symmetric matrices. Numer. Math. 4, 354–361 (1962).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Wilkinson, J. H.Calculation of the eigenvectors of a symmetric tridiagonal matrix by inverse iteration. Numer. Math. 4, 368–376 (1962).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Wilkinson, J. H.The algebraic eigenvalue problem. London: Oxford University Press 1965.zbMATHGoogle Scholar
  7. 7.
    Peters, G., and J. H. Wilkinson. The calculation of specified eigenvectors by inverse iteration. Cf. 11/18.Google Scholar
  8. 8.
    Reinsch, C, and F. L. Bauer. Rational QR transformation with Newton shift for symmetric tridiagonal matrices. Numer. Math. 11, 264–272 (1968). Cf. II/6.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • R. S. Martin
  • C. Reinsch
  • J. H. Wilkinson

There are no affiliations available

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