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1. USING AROMAS TO SEARCH FOR PRESERVED MEASURES AND INTEGRALS IN KAHAN'S METHOD NSTL国家科技图书文献中心

Bogfjellmo, Geir |  Celledoni, Elena... -  《Mathematics of computation》 - 2024,93(348) - 1633~1653 - 共21页

摘要:. 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 a...
关键词: B-series methods |  integrability |  preservation of integrals and measures |  Darboux polynomials |  trees |  aromatic trees |  DISCRETIZATION

2. A NUMERICAL ALGORITHM FOR C-2-SPLINES ON SYMMETRIC SPACES SCIE Web of Science核心 SCOPUS Scopus数据库 NSTL国家科技图书文献中心

Bogfjellmo, Geir |  Modin, Klas... -  《SIAM Journal on Numerical Analysis》 - 2018,56(4) - 2623~2647 - 共25页

摘要: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...
关键词: De Casteljau |  cubic spline |  Riemannian symmetric space |  Bezier curve

3. The Lie Group Structure of the Butcher Group SCOPUS Scopus数据库 SCIE Web of Science核心 NSTL国家科技图书文献中心

Bogfjellmo, Geir |  Schmeding, Alexander -  《Foundations of computational mathematics》 - 2017,17(1) - 127~159 - 共33页

摘要:The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge-Kutta methods. In the present paper, we complement the algebraic treatment ...
关键词: Butcher group |  Infinite-dimensional Lie group |  Hopf algebra of rooted trees |  Regularity of Lie groups |  Symplectic methods

4. The Tame Butcher Group SCIE Web of Science核心 SCOPUS Scopus数据库 NSTL国家科技图书文献中心

Bogfjellmo, Geir |  Schmeding, Alexander -  《Journal of Lie theory》 - 2016,26(4) - 1107~1144 - 共38页

摘要:The Butcher group is a powerful tool for analysing integration methods for ordinary differential equations, in particular Runge-Kutta methods. Recently, a natural Lie group structure has been construc...
关键词: Butcher group |  infinite-dimensional Lie group |  Silva space |  regularity of Lie groups |  B-series |  group of germs of diffeomorphisms

5. High-Order Symplectic Partitioned Lie Group Methods NSTL国家科技图书文献中心

Bogfjellmo, Geir |  Marthinsen, Hakon -  《Foundations of computational mathematics》 - 2016,16(2) - 493~530 - 共38页

摘要:In this article, a unified approach to obtain symplectic integrators on from Lie group integrators on a Lie group is presented. The approach is worked out in detail for symplectic integrators based on...
关键词: Symplectic integrators |  Lie groups |  Order theory

6. CHARACTER GROUPS OF HOPF ALGEBRAS AS INFINITE-DIMENSIONAL LIE GROUPS NSTL国家科技图书文献中心

Bogfjellmo, Geir |  Dahmen, Rafael... -  《Annales de l'Institut Fourier》 - 2016,66(5) - 2101~2155 - 共55页

摘要:In this article character groups of Hopf algebras are studied from the perspective of infinite-dimensional Lie theory. For a graded and connected Hopf algebra we obtain an infinite-dimensional Lie gro...
关键词: real analytic |  infinite-dimensional Lie group |  Hopf algebra |  continuous inverse algebra |  Butcher group |  weakly complete space |  pro-Lie group

7. Hamiltonian B-series and a Lie algebra of non-rooted trees SCOPUS Scopus数据库 SCIE Web of Science核心 NSTL国家科技图书文献中心

Bogfjellmo, Geir |  Curry, Charles... -  《Numerische Mathematik》 - 2017,135(1) - 97~112 - 共16页

摘要:The conditions for a B-series to be a Hamiltonian vector field imply that it may be given as a series indexed by free trees, i.e. trees without root. At present, the pre-Lie structure of rooted trees ...
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