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In this work, the geodesic equations and their numerical solution in Cartesian coordinates on an oblate spheroid, presented by Panou and Korakitis (2017), are generalized on a triaxial ellipsoid. A new exact analytical method and a new…
Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian…
Direct seismic imaging of sub-surface flow, sound-speed and magnetic field is crucial for predicting flux tube emergence on the solar surface, an important ingredient for space weather. The sensitivity of helioseismic mode-amplitude…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
Spatial data collected worldwide at a huge number of locations are frequently used in environmental and climate studies. Spatial modelling for this type of data presents both methodological and computational challenges. In this work we…
We consider the problem of finding embedded closed geodesics on the two-sphere with an incomplete metric defined outside a point. Various techniques including curve shortening methods are used.
We study the estimation of quadratic Sobolev-type integral functionals of an unknown density on the unit sphere. The functional is defined through fractional powers of the Laplace--Beltrami operator and provides a global measure of…
A single spherical antenna is capable of measuring the direction and polarization of a gravitational wave. It is possible to solve the inverse problem using only linear algebra even in the presence of noise. The simplicity of this solution…
The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encountered in practical astronomy is the lack of full sky coverage in the available data. For example,…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
Numerical integration on spheres, including the computation of the areas of spherical triangles, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We…
We present a generalized algorithm based on a spherical harmonics expansion method for efficient computation of the three-dimensional gravitational potential on a multi-patch grid in spherical geometry. Instead of solving for the…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
This paper presents a geometric approach to the classical isoperimetric problem by analysing the efficiency of regular polygons in enclosing maximum area for a fixed perimeter. Using efficiency metrics, it proves that regular polygons…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
One of the few methods for generating efficient function spaces for multi-D Schrodinger eigenproblems is given by Garashchuk and Light in J.Chem.Phys. 114 (2001) 3929. Their Gaussian basis functions are wider and sparser in high potential…
We present a method for obtaining efficient probabilistic solutions to geostatistical and linear inverse problems in spherical geometry. Our Spherical Direct Sequential Simulation (SDSSIM) framework combines information from possibly noisy…
Pose-Graph optimization is a crucial component of many modern SLAM systems. Most prominent state of the art systems address this problem by iterative non-linear least squares. Both number of iterations and convergence basin of these…
To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and…