Related papers: Classical multivariate Hermite coordinate interpol…
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…
It is shown that Hermite polynomials satisfy a Bessel type orthogonality relation, based on the zeros of a single index Hermite polynomial and with a finite integration interval. Because of the role of non-symmetric zeros in the final…
This paper is concerned with Lagrange interpolation by total degree polynomials in moderate dimensions. In particular, we are interested in characterising the optimal choice of points for the interpolation problem, where we define the…
A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike…
Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
We propose an efficient and easy-to-implement gradient-enhanced least squares Monte Carlo method for computing price and Greeks (i.e., derivatives of the price function) of high-dimensional American options. It employs the sparse Hermite…
The classical Hermite-Biehler theorem describes possible zero sets of complex linear combinations of two real polynomials whose zeros strictly interlace. We provide the full characterization of zero sets for the case when this interlacing…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to…
The concepts of evaluation and interpolation are extended from univariate skew polynomials to multivariate skew polynomials, with coefficients over division rings. Iterated skew polynomial rings are in general not suitable for this purpose.…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Interpolation-based techniques become popular in recent years, as they can improve the scalability of existing verification techniques due to their inherent modularity and local reasoning capabilities. Synthesizing Craig interpolants is the…
Multiple Hermite polynomials are an extension of the classical Hermite polynomials for which orthogonality conditions are imposed with respect to $r>1$ normal (Gaussian) weights $w_j(x)=e^{-x^2+c_jx}$ with different means $c_j/2$, $1 \leq j…
In this paper, we introduce some difference sequence spaces in bigeometric calculus. We determine the $\alpha$-duals of these sequence spaces and study their matrix transformations. We also develop an interpolating polynomial in bigeometric…
The effective formulas reducing the two-dimensional Hermite polynomials to the classical (one-dimensional) orthogonal polynomials are given. New one-parameter generating functions for these polynomials are derived. Asymptotical formulas for…
In order to construct a $C^1$-quadratic spline over an arbitrary triangulation, one can split each triangle into 12 subtriangles, resulting in a finer triangulation known as the Powell-Sabin 12-split. It has been shown previously that the…
Interpolation is a fundamental technique in scientific computing and is at the heart of many scientific visualization techniques. There is usually a trade-off between the approximation capabilities of an interpolation scheme and its…
In the paper, the planar polynomial geometric interpolation of data points is revisited. Simple sufficient geometric conditions that imply the existence of the interpolant are derived in general. They require data points to be convex in a…