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Showing 1 to 5 of 5 for “"Geometric integration"”.
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Adaptive Geometric Numerical Integration of Mechanical Systems
… thesis is about structure preserving numerical integration of initial value problems, i.e., so called geometric numerical integrators. In particular, we are interested in how time-step adaptivity can be achieved in conjunction with structure preserving properties without destroying the good long …
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Mathematical Aspects of Field Theory: Nahm's Equations and Jacobi Forms
… multimonopole in Yang-Mills theory. The algebro-geometric integration method is to construct solutions via a linear flow in the Jacobian of the spectral curve associated to the Lax pair. We construct a frame of sections of this linear flow, which allows us to obtain exact solutions to Nahm's …
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Geometric numerical integration for optimisation
In this thesis, we study geometric numerical integration for the optimisation of various classes of functionals. Numerical integration and the study of systems of differential equations have received increased attention within the optimisation community in the last decade, as a means for devising …
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General and Efficient Bayesian Computation through Hamiltonian Monte Carlo Extensions
… of measure-valued differential inclusions.</p><p>Geometrically tempered HMC (GTHMC) presented in Chapter 3 improves HMC’s performance on multi-modal target distributions. The efficiency improvement is achieved through differential geometric techniques, relating a target distribution …
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Constrained Optimization on SO(3), via Pseudospectral Collocation
… optimization techniques to preserve its geometric structure. Riemannian optimization is enabled by mapping problems to the tangent space through equivariant transformations, with the Cayley map providing a computationally efficient coordinate representation. The resulting discretized …