Abstract
We consider numerical schemes for simulating diffusions that evolve in SO(n) and SE(n). Surprisingly, schemes based on the exponential Rodrigues formula have conditioning problems, and we develop for the first time reliable schemes based on diagonal Pade approximants. A crucial feature is that the simulated trajectories lie in the respective manifolds. Also we develop what appear to be the first results guaranteeing first order convergence in mean uniform squared error. The algorithms are illustrated with simulations.
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