Quantum statistical calculations and symplectic corrector algorithms

Quantum statistical calculations and symplectic corrector algorithms.

The quantum partition function at finite temperature requires computing the trace of the imaginary time propagator. For numerical and Monte Carlo calculations, the propagator is usually split into its kinetic and potential parts. A higher-order splitting will result in a higher-order convergent algorithm. At imaginary time, the kinetic energy propagator is usually the diffusion Green's function...

Physics of symplectic integrators: perihelion advances and symplectic corrector algorithms.

Symplectic integrators evolve dynamical systems according to modified Hamiltonians whose error terms are also well-defined Hamiltonians. The error of the algorithm is the sum of each error Hamiltonian's perturbation on the exact solution. When symplectic integrators are applied to the Kepler problem, these error terms cause the orbit to precess. In this work, by developing a general method of c...

Statistical calculations at scale using machine learning algorithms and emulation

As the size of datasets grows, the majority of interesting statistical models become inaccessible because they scale quadratically or worse. For some problems fast algorithms exist that converge to the desired model of interest. But this is rarely true: we often really want to use a complex model. Beyond simply discarding data, how can the model be made to run, and efficiently use the informati...

Modified Quantum-Statistical Calculations for Atomic Electron Densities

On Mehrotra-Type Predictor-Corrector Algorithms

In this paper we discuss the polynomiality of Mehrotra-type predictor-corrector algorithms. We consider a variant of the original prototype of the algorithm that has been widely used in several IPM based optimization packages, for which no complexity result is known to date. By an example we show that in this variant the usual Mehrotra-type adaptive choice of the parameter μ might force the alg...