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» On the Hopf Algebraic Structure of Lie Group Integrators
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FOCM
2008
73views more  FOCM 2008»
9 years 4 months ago
On the Hopf Algebraic Structure of Lie Group Integrators
Hans Z. Munthe-Kaas, Will M. Wright
FOCM
2006
76views more  FOCM 2006»
9 years 4 months ago
The Hopf Algebra of Rooted Trees, Free Lie Algebras, and Lie Series
We present an approach that allows performing computations related to the Baker-Campbell-Haussdorff (BCH) formula and its generalizations in an arbitrary Hall basis, using labeled...
A. Murua
FOCM
2010
143views more  FOCM 2010»
9 years 2 months ago
Algebraic Structures of B-series
B-series are a fundamental tool in practical and theoretical aspects of numerical integrators for ordinary differential equations. A composition law for B-series permits an elega...
Philippe Chartier, Ernst Hairer, Gilles Vilmart
CDC
2009
IEEE
143views Control Systems» more  CDC 2009»
9 years 8 months ago
Control interpretations of products in the Hopf algebra
Abstract— Families of differential operators, like those defining affine, generally nonlinear, control systems are known to have natural Hopf algebra structures. These provide ...
Matthias Kawski
CDC
2008
IEEE
117views Control Systems» more  CDC 2008»
9 years 10 months ago
A hopf-algebraic formula for compositions of noncommuting flows
Abstract— The Chen-Fliess series is known to be an exponential Lie series. Previously explicit formulas for the iterated integral coefficients were known only for its factorizat...
Eric Gehrig, Matthias Kawski
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