Related papers: About one method for constructing Hermite trigonom…
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
We propose a multi-moment method for one-dimensional hyperbolic equations with smooth coefficient and piecewise constant coefficient. The method is entirely based on the backward characteristic method and uses the solution and its…
We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural…
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…
In this work, we introduce a novel Hermite method to handle Maxwell's equations for nonlinear dispersive media. The proposed method achieves high-order accuracy and is free of any nonlinear algebraic solver, requiring solving instead small…
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization takes the form of an approximate generalized LU/LDL…
We consider the problem of computing univariate polynomial matrices over a field that represent minimal solution bases for a general interpolation problem, some forms of which are the vector M-Pad\'e approximation problem in [Van Barel and…
It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which is still presented in its classical form in modern reference works, is valid if and only if a…
A description of Orthogonal Tensor Hermite Polynomials in 3-D is presented. These polynomials, as introduced by Grad in 1949 [1], can be used to obtain a series solution to the Boltzmann Transport Equation. The properties that are explored…
Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the…
We propose an implementation of a method based on Fourier analysis to obtain the Floquet characteristic exponents for periodic homogeneous linear systems, which shows a high precision. This implementation uses a variational principle to…
An algorithm is designed which decomposes a tropical univariate rational function into a composition of tropical binomials and trinomials. When a function is monotone, the composition consists just of binomials. Similar algorithms are…
We prove a generalization of the Kibble--Slepian formula (for Hermite polynomials) and its unitary analogue involving the $2$D Hermite polynomials recently proved in \cite{Ism4}. We derive integral representations for the $2$D Hermite…
In this work, we develop a constructive method for deriving four structure relations and a fourth-order linear differential equation satisfied by Laguerre-Hahn orthogonal polynomial sequences. The method relies on a combination of structure…
In this article, we solve the connection problem of the Hermite polynomials with the classical continuous orthogonal polynomials belonging to Askey scheme, using the hypergeometric functions method combined is with the work the Fields and…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
A general family of matrix valued Hermite type orthogonal polynomials is introduced and studied in detail by deriving Pearson equations for the weight and matrix valued differential equations for these matrix polynomials. This is used to…
We have recently described the implementation of atomic electronic structure calculations within the finite element method with numerical radial basis functions of the form $\chi_{\mu}(r)=r^{-1}B_{\mu}(r)$, where high-order Lagrange…
We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic…