Related papers: On the efficiency and accuracy of interpolation me…
Optics naturally provides us with some powerful mathematical operations. Here we experimentally demonstrate that during reflection or refraction at a single optical planar interface, the optical computing of spatial differentiation can be…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
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 this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneous case. The numerical schemes for these two settings are…
B-splines are widely used in the fields of reverse engineering and computer-aided design, due to their superior properties. Traditional B-spline surface interpolation algorithms usually assume regularity of the data distribution. In this…
We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we…
We present a new way to merge any two point distribution approaches using distance fields. Our new process allows us to produce digital stippling that fills areas with stipple dots without visual artifacts as well as includes clear linear…
Theoretical stellar spectra rely on model stellar atmospheres computed based on our understanding of the physical laws at play in the stellar interiors. These models, coupled with atomic and molecular line databases, are used to generate…
Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
A fast algorithm for B-splines in mixed models is presented. B-splines have local support and are computational attractive, because the corresponding matrices are sparse. A key element of the new algorithm is that the local character of…
We propose a new analysis of convergence for a $k$th order ($k\ge 1$) finite element method, which is applied on Bakhvalov-type meshes to a singularly perturbed two-point boundary value problem. A novel interpolant is introduced, which has…
The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction by means of B-splines and results of simulink-modeling is presented. The advantages of this paper is that…
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
Three forms of representation of trigonometric interpolation splines are considered, in particular, the representation by the coefficients of the interpolation trigonometric polynomial, the representation by trigonometric B-splines, which…
Spectral methods provide an elegant and efficient way of numerically solving differential equations of all kinds. For smooth problems, truncation error for spectral methods vanishes exponentially in the infinity norm and $L_2$-norm.…
In this paper a local approximation method on the sphere is presented. As interpolation scheme we consider a partition of unity method, such as the modified spherical Shepard's method, which uses zonal basis functions (ZBFs) plus spherical…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
A trigonometric interpolation algorithm for non-periodic functions has been recently proposed and applied to study general ordinary differential equation (ODE). This paper enhances the algorithm to approximate functions in $2$-dim space.…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…