Related papers: Convergent Interpolation to Cauchy Integrals over …

Let $\widehat\sigma$ be a Cauchy transform of a possibly complex-valued Borel measure $\sigma$ and $\{p_n\}$ be a system of orthonormal polynomials with respect to a measure $\mu$, $\mathrm{supp}(\mu)\cap\mathrm{supp}(\sigma)=\varnothing$.…

We develop a numerical approach for computing the additive, multiplicative and compressive convolution operations from free probability theory. We utilize the regularity properties of free convolution to identify (pairs of) `admissible'…

The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…

We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…

Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…

For a compact subset $K$ of the complex plane $\mathbb C,$ let $C(K)$ denote the algebra of continuous functions on $K$. For an open subset $U \subset K,$ let $A(K,U) \subset C(K)$ be the algebra of functions that are analytic in $U.$ We…

In a series of papers (Lombardi & Schneider 2001, 2002) we studied in detail the statistical properties of an interpolation technique widely used in astronomy. In particular, we considered the average interpolated map and its covariance…

One frequently needs to interpolate or approximate gradients on simplicial meshes. Unfortunately, there are very few explicit mathematical results governing the interpolation or approximation of vector-valued functions on Delaunay meshes in…

We give the strong asymptotic of Cauchy biorthogonal polynomials under the assumption that the defining measures are supported on non intersecting intervals of the real line and satisfy Szeg\H{o}'s condition. The biorthogonal polynomials…

In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…

Complex signed measures of finite total variation are a powerful signal model in many applications. Restricting to the $d$-dimensional torus, finitely supported measures allow for exact recovery if the trigonometric moments up to some order…

The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there…

For all n large enough, we show uniqueness of a critical point in best rational approximation of degree n, in the L^2-sense on the unit circle, to functions f, where f is a sum of a Cauchy transform of a complex measure \mu supported on a…

The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…

We present a nodal interpolation method to approximate a subdivision model. The main application is to model and represent curved geometry without gaps and preserving the required simulation intent. Accordingly, we devise the technique to…

Methods of Pad\'e approximation are used to analyse a multivariate Markov transform which has been recently introduced by the authors, and which is generalizing the well-known in Spectral theory Stieltjes transform (Markov function) of…

We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…

We prove that the sequence of cones of metric measure spaces converges if the sequence of base spaces converges in Gromov's box, concentration, and weak topologies. As an application, we show that the generalized Cauchy distribution with…

In periodic media gap solitons with frequencies inside a spectral gap but close to a spectral band can be formally approximated by a slowly varying envelope ansatz. The ansatz is based on the linear Bloch waves at the edge of the band and…

The question of adaptive mesh generation for approximation by splines has been studied for a number of years by various authors. The results have numerous applications in computational and discrete geometry, computer aided geometric design,…