A mixed interpolation-regression method for numerical integration on some planar domains
Numerical Analysis
2026-04-28 v1 Numerical Analysis
Abstract
In this contribution we introduce a mixed interpolation-regression operator for functions defined in some domains of the plane. We focus the attention on the ellipse, an annulus and a polygon. An upper bound for such an operator is obtained. Cubature formulas for weight functions defined in such domains are studied. The performance of the above interpolation-regression methods is illustrated with some numerical examples taking into account the variations of the dimension of the interpolation and the regression part, respectively.
Cite
@article{arxiv.2604.24748,
title = {A mixed interpolation-regression method for numerical integration on some planar domains},
author = {Ruymán Cruz-Barroso and Lidia Fernández and Francisco Marcellán and Juan Antonio Villegas},
journal= {arXiv preprint arXiv:2604.24748},
year = {2026}
}