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We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…

Complex Variables · Mathematics 2025-04-10 Ludovico Bruni Bruno , Federico Piazzon

The aim of the paper is to present Hermite-type multiwavelets satisfying the vanishing moment property with respect to elements in the space spanned by exponentials and polynomials. Such functions satisfy a two-scale relation which is…

Numerical Analysis · Mathematics 2017-07-11 Mariantonia Cotronei , Nada Sissouno

Motivated by classical results of approximation theory, we define an Hermite-type interpolation in terms of $n$-dimensional subspaces of the space of $n$ times continuously differentiable functions. In the main result of this paper, we…

Classical Analysis and ODEs · Mathematics 2024-12-12 Ali Hasan Ali , Zsolt Páles

In this work we construct an Hermite interpolant starting from basis functions that satisfy a Lagrange property. In fact, we extend and generalise an iterative approach, introduced by Cirillo and Hormann (2018) for the Floater-Hormann…

Numerical Analysis · Mathematics 2023-09-26 Giacomo Elefante

The problem of barycentric Hermite interpolation is highly susceptible to overflows or underflows. In this paper, based on Sturm-Liouville equations for Jacobi orthogonal polynomials, we consider the fast implementation on the second…

Numerical Analysis · Mathematics 2014-06-05 Shuhuang Xiang , Guo He

In this paper, we consider the particular case of the general rational Hermite interpolation problem where only the value of the function is interpolated at some points, and where the function and its first derivatives agree at the origin.…

Numerical Analysis · Mathematics 2012-09-25 Claude Brezinski , Michela Redivo-Zaglia

Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper…

Classical Analysis and ODEs · Mathematics 2024-05-22 Mustapha Raissouli , Lahcen Tarik , Mohamed Chergui

We present a Hermite interpolation based partial differential equation solver for Hamilton-Jacobi equations. Many Hamilton-Jacobi equations have a nonlinear dependency on the gradient, which gives rise to discontinuities in the derivatives…

Numerical Analysis · Mathematics 2022-06-14 Allen Alvarez Loya , Daniel Appelö

Accurate interpolation of functions and derivatives is crucial in solving partial differential equations (PDEs). The Radial Basis Function (RBF) method has become an extremely popular and robust approach for interpolation on scattered data.…

Numerical Analysis · Mathematics 2025-05-23 Amirhossein Fashamiha , David Salac

Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…

Instrumentation and Methods for Astrophysics · Physics 2025-01-24 Alexander J. Dittmann

This paper presents a novel method for polynomial approximation (Hermite approximation) using the fusion of value and derivative information. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance…

Numerical Analysis · Mathematics 2019-03-27 Roland Ritt , Matthew Harker , Paul O'Leary

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…

Numerical Analysis · Mathematics 2019-02-13 V. P. Denysiuk

A common problem in Bayesian inference is the sampling of target probability distributions at sufficient resolution and accuracy to estimate the probability density, and to compute credible regions. Often by construction, many target…

Computation · Statistics 2020-02-20 Alvin J. K. Chua

The accuracy and effectiveness of Hermite spectral methods for the numerical discretization of partial differential equations on unbounded domains, are strongly affected by the amplitude of the Gaussian weight function employed to describe…

Numerical Analysis · Mathematics 2021-04-07 Lorella Fatone , Daniele Funaro , Gianmarco Manzini

Given a system of triangles in the plane $\mathbb{R}^2$ along with given data of function and gradient values at the vertices, we describe the general pattern of local linear methods invoving only four smooth standard shape functions which…

Numerical Analysis · Mathematics 2023-08-30 L. L. Stachó

Spline interpolation has been used in several applications due to its favorable properties regarding smoothness and accuracy of the interpolant. However, when there exists a discontinuity or a steep gradient in the data, some artifacts can…

Numerical Analysis · Mathematics 2021-12-21 Francesc Aràndiga , Antonio Baeza , Dionisio F. Yáñez

When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…

Machine Learning · Statistics 2018-07-03 F. Patricia Medina , Linda Ness , Melanie Weber , Karamatou Yacoubou Djima

The Gromov-Wasserstein (GW) transport problem is a relaxation of classic optimal transport, which seeks a transport between two measures while preserving their internal geometry. Due to meeting this theoretical underpinning, it is a…

Numerical Analysis · Mathematics 2024-03-14 Florian Beier , Robert Beinert

Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical…

Numerical Analysis · Mathematics 2024-08-12 Bin Han

We present a novel approach to Riemannian interpolation on the Grassmann manifold. Instead of relying on the Riemannian normal coordinates, i.e. the Riemannian exponential and logarithm maps, we approach the interpolation problem with an…

Numerical Analysis · Mathematics 2025-06-23 Rasmus Jensen , Ralf Zimmermann