On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
High order Runge-Kutta methods on manifolds
proceedings of the on Numerical analysis of hamiltonian differential equations
Approximating the exponential from a Lie algebra to a Lie group
Mathematics of Computation
Generalized Polar Decompositions for the Approximation of the Matrix Exponential
SIAM Journal on Matrix Analysis and Applications
Efficient Computation of the Matrix Exponential by Generalized Polar Decompositions
SIAM Journal on Numerical Analysis
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In this paper we explore the computation of the matrix exponential in a manner that is consistent with Lie group structure. Our point of departure is the decomposition of Lie algebra as the semidirect product of two Lie subspaces and an application of the Baker-Campbell-Hausdorff formula. Our results extend the results in Iserles and Zanna (2005) [2], Zanna and Munthe-Kaas(2001/02) [4] to a range of Lie groups: the Lie group of all solid motions in Euclidean space, the Lorentz Lie group of all solid motions in Minkowski space and the group of all invertible (upper) triangular matrices. In our method, the matrix exponential group can be computed by a less computational cost and is more accurate than the current methods. In addition, by this method the approximated matrix exponential belongs to the corresponding Lie group.