Related papers: ARPIST: Provably Accurate and Stable Numerical Int…
We present a novel orbit parameterization in spherical coordinates. This parameterization enables the mixing of varying and invariant orbital parameters, and clarifies the physics of the orbit. It also simplifies the process of placing…
We present and implement an algorithm for computing the invariant circle and the corresponding stable manifolds for 2-dimensional maps. The algorithm is based on the parameterization method, and it is backed up by an a-posteriori theorem…
This paper presents an optimised algorithm implementing the method of slices for analysing the stability of slopes. The algorithm adopts an improved physically based parameterisation of slip lines according to their geometrical…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…
The Spherical Geometry Algorithm (SGA) demonstrates superior capability in achieving efficient and precise spaceborne SAR image formation processing, even under challenging imaging conditions including non-linear radar trajectories and…
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an…
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…
The Navier equation is the governing equation of elastic waves, and computing its solution accurately and rapidly has a wide range of applications in geophysical exploration, materials science, etc. In this paper, we focus on the efficient…
We propose a numerical method to compute the inertial modes of a container with near-spherical geometry based on the fully spectral discretisation of the angular and radial directions using spherical harmonics and Gegenbauer polynomial…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…
We propose an effective subspace selection scheme as a post-processing step to improve results obtained by sparse subspace clustering (SSC). Our method starts by the computation of stable subspaces using a novel random sampling scheme. Thus…
Our present investigation is motivated essentially by several interesting applications of generalized hypergeometric functions of one, two and more variables. The hypergeometric functions are potentially useful and have widespread…
Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…
In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal…
Many popular methods for the calculation of chemical potentials rely on the insertion of test particles into the target system. In the case of liquids and liquid mixtures, this procedure increases in difficulty upon increasing density or…
In this paper, we propose a new technique named \textit{Stochastic Path-Integrated Differential EstimatoR} (SPIDER), which can be used to track many deterministic quantities of interest with significantly reduced computational cost. We…
This work presents a novel framework for spherical mesh parameterization. An efficient angle-preserving spherical parameterization algorithm is introduced, which is based on dynamic Yamabe flow and the conformal welding method with solid…
In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…
Extracting stellar fundamental parameters from SPectro-Interferometric (SPI) data requires reliable estimates of observables and with robust uncertainties (visibility, triple product, phase closure). A number of fine calibration procedures…