106 citations · 677 across the 72 of their papers we have counts for
5 papers · 2 filters
Properties of Hamiltonian Variational Integrators
Jeremy M. Schmitt, Melvin Leok
Discrete Hamiltonian variational integrators are derived from Type II and Type III generating functions for symplectic maps, and in this paper we establish a variational error anal…
Embedding-Based Interpolation on the Special Orthogonal Group
Evan S. Gawlik, Melvin Leok
We study schemes for interpolating functions that take values in the special orthogonal group . Our focus is on interpolation schemes obtained by embedding in a line…
Computing the Fréchet Derivative of the Polar Decomposition
Evan S. Gawlik, Melvin Leok
We derive iterative methods for computing the Fréchet derivative of the map which sends a full-rank matrix to the factor in its polar decomposition , where has or…
Interpolation on Symmetric Spaces via the Generalized Polar Decomposition
Evan Gawlik, Melvin Leok
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is…
Variational integrators for interconnected Lagrange-Dirac systems
Helen Parks, Melvin Leok
Interconnected systems are an important class of mathematical models, as they allow for the construction of complex, hierarchical, multiphysics, and multiscale models by the interc…