Phase fitting has been extensively used during the last years to improve the behaviour of numerical integrators on oscillatory problems. In this work, the benefits of the phase fitting technique are embedded in discrete Lagrangian integrators. The results show improved accuracy and total energy behaviour in Hamiltonian systems. Numerical tests on the long term integration (10 periods) of the 2-...

The K-means algorithm is very popular in the machine learning community due to its inherent simplicity. However in its basic form it is not suitable for use in problems which contain periodic attributes, such as oscillator phase, hour of day or directional heading. A commonly used technique of trigonometrically encoding periodic input attributes to artificially generate the required topology in...

This vignette presents a brief review about the existing approaches for the post-hoc analysis of interactions in factorial experiments, and describes how to perform some of the cited calculations and tests with the functions of the package phia in R. Those functions include the calculation and plotting of cell means, and testing simple effects, residual effects, and interaction contrasts, among...

In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta RK methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase...