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Commutator-free Lie group methods

- E. Celledoni, A. Marthinsen, B. Owren
- MathematicsFuture Gener. Comput. Syst.
- 1 April 2003

Computations in a free Lie algebra

- H. Munthe-Kaas, B. Owren
- MathematicsPhilosophical Transactions of the Royal Society…
- 15 April 1999

Many numerical algorithms involve computations in Lie algebras, like composition and splitting methods, methods involving the Baker–Campbell–Hausdorff formula and the recently developed Lie group… Expand

Deep learning as optimal control problems: models and numerical methods

- M. Benning, E. Celledoni, Matthias Joachim Ehrhardt, B. Owren, C. Schönlieb
- Computer ScienceJournal of Computational Dynamics
- 11 April 2019

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Runge-Kutta Methods Adapted to Manifolds and Based on Rigid Frames

- B. Owren, A. Marthinsen
- Mathematics
- 1 March 1999

We consider numerical integration methods for differentiable manifolds as proposed by Crouch and Grossman. The differential system is phrased by means of a system of frame vector fields E1, ... , En… Expand

Energy-preserving Runge-Kutta methods

- E. Celledoni, R. McLachlan, D. McLaren, B. Owren, G. Quispel, W. Wright
- Computer Science, Mathematics
- 1 July 2009

We show that while Runge-Kutta methods cannot preserve polynomial invariants in gen- eral, they can preserve polynomials that are the energy invariant of canonical Hamiltonian systems.

A General Framework for Deriving Integral Preserving Numerical Methods for PDEs

- Morten Dahlby, B. Owren
- Mathematics, Computer ScienceSIAM J. Sci. Comput.
- 16 September 2010

A general procedure for constructing conservative numerical integrators for time-dependent partial differential equations is presented. In particular, linearly implicit methods preserving a time… Expand

The Newton Iteration on Lie Groups

- B. Owren, B. Welfert
- Mathematics
- 1 March 2000

We define the Newton iteration for solving the equation f(y) = 0, where f is a map from a Lie group to its corresponding Lie algebra. Two versions are presented, which are formulated independently of… Expand

Derivation of Efficient, Continuous, Explicit Runge-Kutta Methods

- B. Owren, M. Zennaro
- Computer Science, MathematicsSIAM J. Sci. Comput.
- 1 November 1992

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B-series and Order Conditions for Exponential Integrators

- H. Berland, B. Owren, B. Skaflestad
- Mathematics, Computer ScienceSIAM J. Numer. Anal.
- 1 April 2005

TLDR

On the Implementation of Lie Group Methods on the Stiefel Manifold

- E. Celledoni, B. Owren
- Computer Science, MathematicsNumerical Algorithms
- 1 April 2003

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