Recent progress on univariate and multivariate polynomial and spline quasi-interpolants
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Abstract
Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods.
Cite
@article{arxiv.math/0405033,
title = {Recent progress on univariate and multivariate polynomial and spline quasi-interpolants},
author = {Paul Sablonniere},
journal= {arXiv preprint arXiv:math/0405033},
year = {2025}
}