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Solution to the Complex Eigenproblem by a Norm Reducing Jacobi Type Method

  • P. J. Eberlein
Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 186)

Abstract

Let C = (c ij ) = A+iZ be a complex n×n matrix having real part A =(a ij ) and imaginary part Z = (z ij ). We construct a complex matrix W = T +iU = W 1 W 2W k as a product of non-singular two dimensional transformations W j such that the off diagonal elements of W -1 CW =C are arbitrarily small1. The diagonal elements of C are now approximations to the eigenvalues and the columns of W are approximations to the corresponding right eigenvectors.

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References

  1. 1.
    Eberlein, P. J., Boothroyd, J.: Solution to the eigenproblem by a norm-reducing Jacobi-type method. Numer. Math. 11, l, 1–12 (1968). Cf. 11/12.CrossRefGoogle Scholar
  2. 2.
    Eberlein, P. J., Boothroyd, J A Jacobi-like method for the automatic computation of eigenvalues and eigenvectors of an arbitrary matrix. J. Soc. Indust. Appl. Math. 10, 1, 74 – 88 (1962).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

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  • P. J. Eberlein

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