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Similarity Reduction of a General Matrix to Hessenberg Form

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

Abstract

With several algorithms for finding the eigensystem of a matrix the volume of work is greatly reduced if the matrix A is first transformed to upper-Hessenberg form, i.e. to a matrix H such that h, ij 0 (i> i+1). The reduction may be achieved in a stable manner by the use of either stabilized elementary matrices or elementary unitary matrices [2].

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References

  1. 1.
    Martin, R. S., C. Reinsch, and J. H. Wilkinson: Householder’s tridiagonalization of a symmetric matrix. Numer. Math. 11, 181 -195 (1968). Cf. II/2.MathSciNetzbMATHCrossRefGoogle Scholar
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    Wilkinson, J. H.: The algebraic eigenvalue problem. London: Oxford University Press 1965-zbMATHGoogle Scholar
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    Parlett, B. N., and C. Reinsch. Balancing a matrix for calculation of eigenvalues and eigenvectors. Numer. Math. 13, 293–304 (1969). Cf. 11/11.MathSciNetzbMATHCrossRefGoogle Scholar
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Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

  • R. S. Martin
  • J. H. Wilkinson

There are no affiliations available

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