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].
Prepublished in Numer. Math. 12, 349 – 368 (1968).
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References
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.
Wilkinson, J. H.: The algebraic eigenvalue problem. London: Oxford University Press 1965-
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Martin, R. S., and J. H. Wilkinson, G.Peters, and J.H.Wilkinson. The QR algorithm for real Hessenberg matrices. Numer. Math. 14, 219–231 (1970). Cf. 11/14.
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© 1971 Springer-Verlag Berlin · Heidelberg
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Martin, R.S., Wilkinson, J.H. (1971). Similarity Reduction of a General Matrix to Hessenberg Form. 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_24
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DOI: https://doi.org/10.1007/978-3-642-86940-2_24
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