Abstract
In a recent paper [4] the triangularization of complex Hessenberg matrices using the LR algorithm was described. Denoting the Hessenberg matrix by H and the final triangular matrix by T we have
where P is the product of all the transformation matrices used in the execution of the LR algorithm. In practice H will almost invariably have been derived from a general complex matrix A using the procedure comhes [3] and hence for some nonsingular S we have
Prepublished in Numer. Math. 16, 181 – 204 (1970).
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References
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Peters, G., Wilkinson, J.H. (1971). Eigenvectors of Real and Complex Matrices by LR and QR triangularizations. 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_26
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DOI: https://doi.org/10.1007/978-3-642-86940-2_26
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