Related papers: Multidimensional intertwining Leja sequences and a…
High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…
We make sharp estimates to obtain a Schwarz type lemma for the symmetrized polydisc $\gn$ and for the extended symmetrized polydisc $\Gn$. We explicitly construct an interpolating function under certain condition. To do so, we followed the…
Padua points is a family of points on the square $[-1,1]^2$ given by explicit formulas that admits unique Lagrange interpolation by bivariate polynomials. The interpolation polynomials and cubature formulas based on the Padua points are…
In this work, we study superconvergence properties for some high-order orthogonal polynomial interpolations.The results are two-folds: When interpolating function values, we identify those points where the first and second derivatives of…
Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
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.
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
We extend Newton and Lagrange interpolation to arbitrary dimensions. The core contribution that enables this is a generalized notion of non-tensorial unisolvent nodes, i.e., nodes on which the multivariate polynomial interpolant of a…
Multilinear interpolation is a powerful tool used in obtaining strong type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear…
In this paper, by means of the classical Lagrange inversion formula, we establish a general nonlinear inverse relations which is a partial solution to the problem proposed in the paper [J. Wang, Nonlinear inverse relations for the Bell…
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of…
High-dimensional Lagrange interpolation plays a pivotal role in finite element methods, where ensuring the unisolvence and symmetry of its interpolation space and nodes set is crucial. In this paper, we leverage group action and group…
Fast Leja points on an interval are points constructed using a discrete modification of the algorithm for constructing Leja points. Not much about fast Leja points has been proven theoretically. We present an asymptotic property of a…
For a polynomial P, we consider the sequence of iterated integrals of ln P(x). This sequence is expressed in terms of the zeros of P(x). In the special case of ln(1 + x^2), arithmetic properties of certain coefficients arising are…
We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are…
Given a convergent sequence of nodes we present a one-dimensional-holomorphic-function version of the Newton interpolation method of polynomials. It also generalises the Taylor and the Laurent formula. In other words, we present an…
In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…
In this article, we introduce the adapted inverse iteration method to generate bicomplex Julia sets associated to the polynomial map $w^2+c$. The result is based on a full characterization of bicomplex Julia sets as the boundary of a…
We formalize a technique for embedding Riemann sufraces properly into \C^2, and we generalize all known embedding results to allow interpolation on prescribed discrete sequences.