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Householder’s Tridiagonalization of a Symmetric Matrix

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Linear Algebra

Part of the book series: Handbook for Automatic Computation ((HDBKAUCO,volume 2))

Abstract

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.

Prepublished in Numer. Math. 11, 181–195 (1968).

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References

  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.

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  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.

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  3. Ortega, J.M.: An error analysis of Householder’s method for the symmetric eigenvalue problem. Numer. Math. 5, 211–225 (1963).

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  4. Wilkinson, J. H.: Householder’s method for symmetric matrices. Numer. Math. 4, 354–361 (1962).

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  5. Wilkinson, J. H.: Calculation of the eigenvectors of a symmetric tridiagonal matrix by inverse iteration. Numer. Math. 4, 368–376 (1962).

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

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  7. Peters, G., and J. H. Wilkinson: The calculation of specified eigenvectors by inverse iteration. Cf. II/18.

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  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.

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Authors
  1. R. S. Martin
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  2. C. Reinsch
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  3. J. H. Wilkinson
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Editor information

Editors and Affiliations

  1. Mathematisches Inst., Techn. Univ., Arcisstr. 21, 8 München 2, Deutschland

    F. L. Bauer (Chief editor) (Chief editor)

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© 1971 Springer-Verlag Berlin Heidelberg

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Martin, R.S., Reinsch, C., Wilkinson, J.H. (1971). Householder’s Tridiagonalization of a Symmetric Matrix. In: Bauer, F.L. (eds) Linear Algebra. Handbook for Automatic Computation, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39778-7_13

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  • DOI: https://doi.org/10.1007/978-3-662-39778-7_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-38854-9

  • Online ISBN: 978-3-662-39778-7

  • eBook Packages: Springer Book Archive

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