Related papers: On Some Generalizations of B-Splines
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We define an indicial polynomial of a $D$-module along an arbitrary subvariety as a generalization of both the classical indicial polynomial for a single linear differential equation and the Bernstein-Sato polynomial of a variety defined by…
Continuous spline functions are defined as piecewise polynomials on the faces of a polyhedral complex that agree on the intersections of two faces. Splines are used in approximation theory and numerical analysis, with applications in data…
Generalizations of the (rank 1) Bannai-Ito algebra are obtained from a refinement of the grade involution of the Lie super algebra $\mathfrak{osp}(1,2)$. A hyperoctahedral extension is derived by using a realization of $\mathfrak{osp}(1,2)$…
We introduce the $B$-Stirling numbers of the first and second kind, which are the coefficients of the potential polynomials when we express them in terms of the monomials and the falling factorials, respectively. These numbers include, as…
Let $R$ be a commutative ring with identity and $G$ a graph. \emph{An extending generalized spline} on $G$ is a vertex labeling $f \in \prod_{v} M_v$ such that at each edge $e=uv$ there is an $R$-module $M_{uv}$ together with homomorphisms…
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.
Spline functions have long been used in numerically solving differential equations. Recently it revives as isogeometric analysis, which uses NURBS for both parametrization and element functions. In this paper, we introduce some multivariate…
We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.
We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…
We give a description, in analytic and geometric terms, of the interpolation sequences for the algebra of entire functions of exponential type which are bounded on the real line.
One of the possible variants of the classification of trigonometric interpolation splines is considered, depending on the chosen convergence factors, the distribution of signs of the basis functions and the interpolation factors. The…
We introduce B-splines on the line of quaternionic order $B_q$ ($q$ in the algebra of quaternions) for the purposes of multi-channel signal and image analysis. The functions $B_q$ are defined first by their Fourier transforms, then as the…
Normal multi-scale transform [4] is a nonlinear multi-scale transform for representing geometric objects that has been recently investigated [1, 7, 10]. The restrictive role of the exact order of polynomial reproduction $P_e$ of the…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
Finite trigonometric Fourier series on a set of discrete equidistant points are considered. A finite system of orthogonal functions that have interpolation and certain differential properties on the period is introduced. Finite Fourier…
Methods of constructing trigonometric fundamental splines with constant sign and sign-changing convergence factors are given. An example and graphics illustrating the concepts of convergence and interpolation grids are given. Some methods…
Physical systems and signals are often characterized by complex functions of frequency in the harmonic-domain. The extension of such functions to the complex frequency plane has been a topic of growing interest as it was shown that specific…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
In this paper a general theory for interpolation methods on a rectangular grid is introduced. By the use of this theory an efficient B-spline based interpolation method for spectral codes is presented. The theory links the order of the…