## Title data

Grüne, Lars ; Karafyllis, Iasson:

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

*In:* Hüper, Knut ; Trumpf, Jochen
(ed.):
Mathematical System Theory : Festschrift in Honor of Uwe Helmke on the Occasion of his 60th Birthday. -
S.l.
: CreateSpace Independent Publishing Platform
,
2013
. - pp. 183-210

## Abstract in another language

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: | Article in a book |
---|---|

Refereed: | Yes |

Institutions of the University: | 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) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne Faculties Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science |

Date Deposited: | 18 Feb 2021 11:56 |

Last Modified: | 23 Mar 2021 09:12 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63195 |