TY - JOUR
T1 - On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift
AU - Nakamura, Y.
AU - Kajiwara, K.
AU - Shiotani, H.
N1 - Funding Information:
The authors would like to thank Professor R. Hirota for stimulating discussions on integrable discretization and its applications. One of the authors (Y.N) was supported in part by Grant-in-Aid for Scientific Research nos. 07210105, 08211106, 08874013 from the Japan Ministry of Education, Science, and Culture.
PY - 1998/9/15
Y1 - 1998/9/15
N2 - An integrable discretization of the Rayleigh quotient gradient system is established. The solution of the discrete gradient system is described explicitly and converges exponentially to the same equilibrium point as that of the continuous gradient system for arbitrary large difference step size. It is shown that the discrete gradient system is essentially equivalent to the power method with a shift of origin for calculating the largest eigenvalue. The power method is then proved to be a discrete gradient method.
AB - An integrable discretization of the Rayleigh quotient gradient system is established. The solution of the discrete gradient system is described explicitly and converges exponentially to the same equilibrium point as that of the continuous gradient system for arbitrary large difference step size. It is shown that the discrete gradient system is essentially equivalent to the power method with a shift of origin for calculating the largest eigenvalue. The power method is then proved to be a discrete gradient method.
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U2 - 10.1016/S0377-0427(98)00084-3
DO - 10.1016/S0377-0427(98)00084-3
M3 - Article
AN - SCOPUS:0032162767
SN - 0377-0427
VL - 96
SP - 77
EP - 90
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 2
ER -