相关论文: Moebius-Invariant Natural Neighbor Interpolation
Interpolation methodologies have been widely used within the domain of indoor positioning systems. However, existing indoor positioning interpolation algorithms exhibit several inherent limitations, including reliance on complex…
The present paper concerns filtered de la Vall\'ee Poussin (VP) interpolation at the Chebyshev nodes of the four kinds. This approximation model is interesting for applications because it combines the advantages of the classical Lagrange…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an…
We study some conformally invariant integral equations using the method of moving spheres.
We show a method to construct isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, and it allows to construct Sturm-Liouville problems with polynomial eigenfunctions…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
We present two methods to interpolate between two given rigid body displacements. Both are based on linear interpolation in the ambient space of well-known curved point models for the group of rigid body displacements. The resulting motions…
In this paper, we propose a trigonometric-interpolation approach for solutions of second order nonlinear ODEs with mixed boundary conditions. The method interpolates secondary derivative $y''$ of a target solution $y$ by a trigonometric…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick-Brown, we define a new invariant called the weighted…
In this paper we propose a new formulation of the Fourier Modal Method based on an alternative treatment of interface conditions allowing us to overcome the effect of the Gibbs phenomenon. Explicit consideration of the interface conditions…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
A method is presented for forming polynomial interpolants on squares and cubes, which are more efficient in the so-called Euclidean degree than other commonly used methods with the same number of collocation points. These methods have…
In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…
A fast and reliable algorithm for the optimal interpolation of scattered data on the torus by multivariate trigonometric polynomials is presented. The algorithm is based on a variant of the conjugate gradient method in combination with the…
In [18] Fournier and Printems establish a methodology which allows to prove the absolute continuity of the law of the solution of some stochastic equations with H\"{o}lder continuous coefficients. This is of course out of reach by using…
We compute invariants for the two-variable M\"obius transformation. In particular we are interested in partial differential equations in two dependent and two independent variables that are kept invariant under this transformation.