Luke Shaw

collaborators

2 papers

math.NA2022

A New Optimality Property of Strang's Splitting

Fernando Casas, Jesús María Sanz-Serna, Luke Shaw

For systems of the form $q ˙ = M^{- 1} p$ , $p ˙ = - A q + f (q)$ , common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems $\dot…

stat.CO2022

Split Hamiltonian Monte Carlo revisited

Fernando Casas, Jesús María Sanz-Serna, Luke Shaw

We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the Hamiltonian $H$ as $H_{0} (θ, p) + U_{1} (θ)$ , where $H_{0}$ is quadratic and $U_{1}$ small. We show that, in general, suc…