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On the Relationship Between Convergence Rates of Discrete and Continuous Dynamical Systems

Raphael Hauser (hauser***at***comlab.ox.ac.uk)
Jelena Nedic (jelena***at***comlab.ox.ac.uk)

Abstract: Considering iterative sequences that arise when the approximate solution $x_k$ to a numerical problem is updated by $x_{k+1} = x_k+v(x_k)$, where $v$ is a vector field, we derive necessary and sufficient conditions for such discrete methods to converge to a stationary point of $v$ at different Q-rates in terms of the differential properties of $v$ and in terms of the asymptotic dynamical behaviour of the associated continuous dynamical system.

Keywords: Q-convergence, superlinear convergence

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Research report NA-04/10, Oxford University Computing Laboratory, May 2004

Download: [Postscript]

Entry Submitted: 06/02/2004
Entry Accepted: 06/02/2004
Entry Last Modified: 06/02/2004

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