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Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms.

Abstract : We present and analyze an abstract step size selection algorithm which ensures asymptotic stability of numerical approximations to asymptotically stable ODEs. A particular implementation of this algorithm is proposed and tested with two numerical examples. The application to ODEs solving nonlinear optimization problems on manifolds is explained and illustrated by means of the Rayleigh flow for computing eigenvalues of symmetric matrices.
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https://hal.inria.fr/hal-00800458
Contributor : Estelle Bouzat <>
Submitted on : Wednesday, March 13, 2013 - 4:39:09 PM
Last modification on : Friday, October 13, 2017 - 5:08:16 PM

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Lars Grüne, Iasson Karafyllis. Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms.. K. Hüper and J. Trumpf. Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday, CreateSpace, pp.183 - 210, 2013, 978-1470044008. ⟨hal-00800458⟩

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