On Rutishausers approach to selfsimilar flows

Watkins DS, Elsner L (1990)
SIAM Journal on matrix analysis and applications 11(2): 301-311.

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Certain variants of the Toda flow are continuous analogues of the QR algorithm and other algorithms for calculating eigenvalues of matrices. This was a remarkable discovery of the early eighties. Until very recently contemporary researchers studying this circle of ideas have been unaware that continuous analogues of the quotient- difference and LR algorithms were already known to Rutishauser in the fifties. Rutishauser's continuous analogue of the quotient- difference algorithm contains the finite, nonperiodic Toda flow as a special case. A nice feature of Rutishauser's approach is that it leads from the (discrete) eigenvalue algorithm to the (continuous) flow by a limitting process. Thus the connection between the algorithm and the flow does not come as a surprise. In this paper it is shown how Rutishauser's approach can be generalized to yield large families of flows in a natural manner. The flows derived include continuous analogues of the LR, QR, SR, and HR algorithms.
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Watkins DS, Elsner L. On Rutishausers approach to selfsimilar flows. SIAM Journal on matrix analysis and applications. 1990;11(2):301-311.
Watkins, D. S., & Elsner, L. (1990). On Rutishausers approach to selfsimilar flows. SIAM Journal on matrix analysis and applications, 11(2), 301-311.
Watkins, D. S., and Elsner, L. (1990). On Rutishausers approach to selfsimilar flows. SIAM Journal on matrix analysis and applications 11, 301-311.
Watkins, D.S., & Elsner, L., 1990. On Rutishausers approach to selfsimilar flows. SIAM Journal on matrix analysis and applications, 11(2), p 301-311.
D.S. Watkins and L. Elsner, “On Rutishausers approach to selfsimilar flows”, SIAM Journal on matrix analysis and applications, vol. 11, 1990, pp. 301-311.
Watkins, D.S., Elsner, L.: On Rutishausers approach to selfsimilar flows. SIAM Journal on matrix analysis and applications. 11, 301-311 (1990).
Watkins, David S., and Elsner, Ludwig. “On Rutishausers approach to selfsimilar flows”. SIAM Journal on matrix analysis and applications 11.2 (1990): 301-311.
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