Related papers: Fast and stable global interpolation based on equi…
A method for 3D interpolation between hard spheres is described. The function to be interpolated could be the charge density between atoms in condensed matter. Its electrostatic potential is found analytically, and so are various integrals.…
Capturing data from dynamic processes through cross-sectional measurements is seen in many fields, such as computational biology. Trajectory inference deals with the challenge of reconstructing continuous processes from such observations.…
We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…
Visual inspections for identifying focusing points in inertial microfluidic flows are prone to misinterpreting stable locations and focusing shifts in the case of non-trivial focusing patterns. We develop and deploy an approach for…
Geodesic distance matrices can reveal shape properties that are largely invariant to non-rigid deformations, and thus are often used to analyze and represent 3-D shapes. However, these matrices grow quadratically with the number of points.…
We present a new image scaling method both for downscaling and upscaling, running with any scale factor or desired size. The resized image is achieved by sampling a bivariate polynomial which globally interpolates the data at the new scale.…
We develop a stable finite difference method for the elastic wave equation in bounded media, where the material properties can be discontinuous at curved interfaces. The governing equation is discretized in second order form by a fourth or…
This paper concerns the stability on the inverse source scattering problem for the one-dimensional Helmholtz equation in a two-layered medium. We show that the increasing stability can be achieved by using multi-frequency wave field at the…
This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
We prove that any stable method for resolving the Gibbs phenomenon - that is, recovering high-order accuracy from the first $m$ Fourier coefficients of an analytic and nonperiodic function - can converge at best root-exponentially fast in…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
The paper establishes an analog Whittaker-Shannon-Kotelnikov sampling theorem with fast decreasing coefficient, as well as a new modification of the corresponding interpolation formula applicable for general type non-vanishing bounded…
The equilibrium points and their linear stability has been discussed in the generalized photogravitational Chermnykh's problem. The bigger primary is being considered as a source of radiation and small primary as an oblate spheroid. The…
Multipoint secant and interpolation methods are effective tools for solving systems of nonlinear equations. They use quasi-Newton updates for approximating the Jacobian matrix. Owing to their ability to more completely utilize the…
In convergence analysis of finite element methods for singularly perturbed reaction--diffusion problems, balanced norms have been successfully introduced to replace standard energy norms so that layers can be captured. In this article, we…
Based on the sampling theorem, interpolation should be conducted by employing the sinc functions as the kernels. Inspired by the fact that the discrete Fourier transform (DFT) is sampled from the discrete time Fourier transform, a fast…