TY  - JOUR
AB  - 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.
DA  - 1990
DO  - 10.1137/0611020
KW  - LR algorithm
KW  - Quotient-difference algorithm
KW  - Self-similar flow
KW  - Toda flow
KW  - QR algorithm
LA  - eng
IS  - 2
M2  - 301
PY  - 1990
SN  - 0895-4798
SP  - 301-311
T2  - SIAM Journal on matrix analysis and applications
TI  - On Rutishauser's approach to self-similar flows
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-17762147
Y2  - 2024-11-22T03:20:08
ER  -