Related papers: Prony's method in several variables
Multivariable generalizations of the continuous Hahn and Wilson polynomials are introduced as eigenfunctions of rational Ruijsenaars type difference systems with an external field.
We characterize the sets of solvability for Hermite multivariate interpolation problems when the sum of multiplicities is at most $2n + 2$, with $n$ the degree of the polynomial space. This result extends an earlier theorem (2000) by one of…
We describe the first results of a project of analyzing in which theories formal proofs can be ex- pressed. We use this analysis as the basis of interoperability between proof systems.
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…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
We describe some examples of classical and explicit h-transforms as particular cases of a general mechanism, which is related to the existence of symmetric diffusion operators having orthogonal polynomials as spectral decomposition.
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
Polynomial regression is widely used and can help to express nonlinear patterns. However, considering very high polynomial orders may lead to overfitting and poor extrapolation ability for unseen data. The paper presents a method for…
In this paper, we study how to quickly compute the <-minimal monomial interpolating basis for a multivariate polynomial interpolation problem. We address the notion of "reverse" reduced basis of linearly independent polynomials and design…
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the…
This paper undertakes a thorough investigation of matrix means interpolation and comparison. We expand the parameter $\vartheta$ beyond the closed interval $[0,1]$ to cover the entire positive real line, denoted as $\mathbb{R}^+$.…
Prony's problem in several variables has attracted some attention recently and provides an interesting combination of polynomial ideal theory with analytic and numeric computations. This note points out further connections to Hankel…
The method of constructing Hermite trigonometric polynomials, which interpolate the values of a certain periodic function and its derivatives up to (including ) the -th ( ) order in nodes of a uniform grid, is considered. The proposed…
We introduce the notion of "special superpolynomials" by putting q=1 in the formulas for reduced superpolynomials. In this way we obtain a generalization of special HOMFLY polynomials depending on one extra parameter t. Special HOMFLY are…
Polynomials known as Multiple Orthogonal Polynomials in a single variable are polynomials that satisfy orthogonality conditions concerning multiple measures and play a significant role in several applications such as Hermite-Pad\'e…
We prove that every multiplier sequence for the Legendre basis which can be interpolated by a polynomial has the form $\{h(k^2+k)\}_{k=0}^{\infty}$, where $h\in\mathbb{R}[x]$. We also prove that a non-trivial collection of polynomials of a…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range 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…
Theory interpolation has found several successful applications in model checking. We present a novel method for computing interpolants for ground formulas in the theory of equality. The method produces interpolants from colored congruence…