相关论文: Spherical Harmonics Interpolation, Computation of …
Interpolation by various types of splines is the standard procedure in many applications. In this paper we shall discuss harmonic spline "interpolation" (on the lines of a grid) as an alternative to polynomial spline interpolation (at…
This paper is concerned with linear stochastic Hamiltonian (LSH) systems subject to random external forces. Their dynamics are modelled by linear stochastic differential equations, parameterised by stiffness, mass, damping and coupling…
This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode…
We report on the design and experimental characterization of a surface-electrode multipole ion trap. Individual microscopic sugar particles are confined in the trap. The trajectories of driven particle motion are compared with a theoretical…
This paper presents a regularization technique for the high order efficient numerical evaluation of nearly singular, principal-value, and finite-part Cauchy-type integral operators. By relying on the Cauchy formula, the Cauchy-Goursat…
This work introduces a surrogate-based model for efficiently estimating the frequency response of dynamic mechanical metamaterials, particularly when dealing with large parametric perturbations and aperiodic substructures. The research…
We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at $L$ using only $L^2$ samples. We obtain the optimal number of samples given by the…
The rich spectral information of the graph Laplacian has been instrumental in graph theory, machine learning, and graph signal processing for applications such as graph classification, clustering, or eigenmode analysis. Recently, the Hodge…
I present an exact and explicit solution to the scalar (Stokes flux intensity) radio interferometer imaging equation on a spherical surface which is valid also for non-coplanar interferometer configurations. This imaging equation is…
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
Performing efficient quantum computer tuneup and calibration is essential for growth in system complexity. In this work we explore the link between facilitating such capabilities and the underlying architecture of the physical hardware. We…
The main result in this paper is an error estimate for interpolation biharmonic polysplines in an annulus $A\left( r_{1},r_{N}\right) $, with respect to a partition by concentric annular domains $A\left( r_{1} ,r_{2}\right) ,$ ....,…
We consider the bi-Laplacian eigenvalue problem for the modes of vibration of a thin elastic plate with a discrete set of clamped points. A high-order boundary integral equation method is developed for efficient numerical determination of…
We consider the approximation of minimal geodesics between two closed sets in $\mathbb{R}^D$ endowed with a smooth Riemannian metric. The continuous problem is formulated as the minimization of the energy functional over piecewise smooth…
Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…
We present a simple algorithm to select multivariate interpolation stencil with a Cartesian grid. We show its applicability by using this algorithm in the embedded boundary method for solving the elliptic interface problem.
Hypergraph learning with $p$-Laplacian regularization has attracted a lot of attention due to its flexibility in modeling higher-order relationships in data. This paper focuses on its fast numerical implementation, which is challenging due…
In graph signal processing, data samples are associated to vertices on a graph, while edge weights represent similarities between those samples. We propose a convex optimization problem to learn sparse well connected graphs from data. We…
It is well known that the Lagrangian and Hamiltonian descriptions of field theories are equivalent at the discrete time level when variational integrators are used. Besides the symplectic Hamiltonian structure, many physical systems exhibit…