Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Bogfjellmo, Geir"'
The Prytz planimeter is a simple mechanical device that historically was used to approximate areas of plane regions. In this article, we present a mathematical description and analysis of the planimeter in terms of sub-Riemannian geometry and in term
Externí odkaz:
http://arxiv.org/abs/2309.02174
The numerical method of Kahan applied to quadratic differential equations is known to often generate integrable maps in low dimensions and can in more general situations exhibit preserved measures and integrals. Computerized methods based on discrete
Externí odkaz:
http://arxiv.org/abs/2209.01094
Autor:
Bogfjellmo, Geir
A novel symplectic integrator for Hamiltonian equations on $S_2^n \times T^{\ast} \RR^m$ is developed and studied. Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltionian manifolds are studied, specifically, algebraic con
Externí odkaz:
http://arxiv.org/abs/1809.06231
Publikováno v:
In Ebrahimi-Fard K., Barbero Linan M. (eds) Discrete Mechanics, Geometric Integration and Lie-Butcher Series. Springer Proceedings in Mathematics & Statistics, vol 267. Springer, Cham (2018), pp. 287-314
Character groups of Hopf algebras appear in a variety of mathematical and physical contexts. To name just a few, they arise in non-commutative geometry, renormalisation of quantum field theory, and numerical analysis. In the present article we review
Externí odkaz:
http://arxiv.org/abs/1711.05963
Autor:
Bogfjellmo, Geir, Schmeding, Alexander
Publikováno v:
Computation and Combinatorics in Dynamics, Stochastics and Control. Abelsymposium 2016. Abel Symposia, vol 13
Character groups of Hopf algebras appear in a variety of mathematical contexts such as non-commutative geometry, renormalisation of quantum field theory, numerical analysis and the theory of regularity structures for stochastic partial differential e
Externí odkaz:
http://arxiv.org/abs/1704.01099
Publikováno v:
SIAM J. Numer. Anal., 56(4), 2623-2647 (2018)
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing need for s
Externí odkaz:
http://arxiv.org/abs/1703.09589
Publikováno v:
Mathematics of Computation; Jul2024, Vol. 93 Issue 348, p1633-1653, 21p
Autor:
Bogfjellmo, Geir
This thesis studies variational problems invariant under a Lie group transformation, and invariant discretizations of these. In chapters two and three, a general method for creating symplectic integrators preserving certain classes of variational sym
Externí odkaz:
http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13143
Autor:
Bogfjellmo, Geir, Schmeding, Alexander
Publikováno v:
J. Lie theory 26 (2016), No. 4, 1107-1144
The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge--Kutta methods. Recently, a natural Lie group structure has been constructed for this group. Unfortunately, the associated to
Externí odkaz:
http://arxiv.org/abs/1509.03452
Autor:
Bogfjellmo, Geir
Aromatic B-series are a generalization of B-series. Some of the operations defined for B-series can be defined analogically for aromatic B-series. This paper derives combinatorial formulas for the composition and substitution laws for aromatic B-seri
Externí odkaz:
http://arxiv.org/abs/1505.01973