Related papers: Multidimensional algebraic interpolations
The main aim of this paper is the study of the general solution of the exceptional Hermite differential equation with fixed partition $\lambda = (1)$ and the construction of minimal surfaces associated with this solution. We derive a linear…
This paper deals with Hermite osculatory interpolating splines. For a partition of a real interval endowed with a refinement consisting in dividing each subinterval into two small subintervals, we consider a space of smooth splines with…
We study a class of overdetermined algebraic systems of equations. We prove that the number of distinct solutions equals to the maximal possible if and only if certain matrices are commuting and semisimple. This gives a characterization of…
Hermite spectral method plays an important role in the numerical simulation of various partial differential equations (PDEs) on unbounded domains. In this work, we study the superconvergence properties of Hermite spectral interpolation,…
The operational calculus associated with special polynomials has proven to be a powerful tool for analyzing and simplifying their properties. This article examines the bivariate degenerate Hermite polynomials with a focus on their…
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…
The multiplication theorem for univariate Hermite polynomials $H_k(\lambda x)$ is well-known. In this paper we generalize this result to multivariate Hermite polynomials ${\rm H}_{\bf k}({\mathbf{\Lambda}}{\bf x};{\mathbf{\Sigma}})$, and…
In this article, the matrix elements of a representation of the 5-dimensional Lie algebra K5 are obtained for the first time. The bivariate degenerate Hermite polynomials Hm(z1, z2|{\tau} ) are considered within the context of this…
We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.
We give operational formulae of Burchnall type involving complex Hermite polynomials. Short proofs of some known formulae are given and new results involving these polynomials, including Nielsen's identities and Runge addition formula, are…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
The method of Whitney interpolation is used to construct, for any real or complex projective algebraic variety, a stratified submersive family of self-maps that yields stratified general position and transversality theorems for…
We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetric multiple zeta values, and polynomial multiple zeta…
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…
There is presented an algorithm for computing the topological degree for a large class of polynomial mappings. As an application there is given an effective algebraic formula for the intersection number of a polynomial immersion M --> R^2m,…
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
Inspired by the work about solutions of a system of real polynomial equations done by Hermite, this paper introduces a Hermitian form, which encodes information about solutions of a system of complex polynomial equations with conjugate…
We present an accurate investigation of the algebraic conditions that the symbols of a univariate, binary, Hermite subdivision scheme have to fulfil in order to reproduce polynomials. These conditions are sufficient for the scheme to…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.