On an integrable discretization of the Rayleigh quotient gradient system and the power method with a shift (Q1298636)

The authors study discretizations of a dynamical system related to Rayleigh quotients which they call Rayleigh quotient gradient system. They introduce a rather weak notion of integrable discretizations where the arising difference equations possess explicit solutions without defining the precise meaning of explicit. They exhibit such a discretization for the Rayleigh quotient gradient system and show that it is essentially equivalent to the power method with a shift for computing the largest eigenvalue. Finally, they show that the power method is a discrete gradient method.