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 2…W 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.
Prepublished in Numer. Math. 14, 232 – 245 (1970).
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References
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.
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).
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Eberlein, P.J. (1971). Solution to the Complex Eigenproblem by a Norm Reducing Jacobi Type Method. In: Bauer, F.L., Householder, A.S., Olver, F.W.J., Rutishauser, H., Samelson, K., Stiefel, E. (eds) Handbook for Automatic Computation. Die Grundlehren der mathematischen Wissenschaften, vol 186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86940-2_28
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DOI: https://doi.org/10.1007/978-3-642-86940-2_28
Publisher Name: Springer, Berlin, Heidelberg
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