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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005661
URN to cite this document: urn:nbn:de:bvb:703-epub-5661-7

Title data

Grüne, Lars ; Karafyllis, Iasson:
Lyapunov function based step size control for numerical ODE solvers with application to optimization algorithms.
Bayreuth , 2013

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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.

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erschienen In: Hüper, Knut ; Trumpf, Jochen (Hrsg.): Mathematical System Theory : Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday. - S.l. : CreateSpace Independent Publishing Platform , 2013 . - S. 183-210
DDC Subjects:	500 Science 500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-5661-7
Date Deposited:	01 Jun 2021 12:13
Last Modified:	01 Jun 2021 12:14
URI:	https://epub.uni-bayreuth.de/id/eprint/5661

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