A mixed interpolation-regression method for numerical integration on some planar domains

TL;DR

This paper introduces a mixed interpolation-regression operator for numerical integration on planar domains like ellipses, annuli, and polygons, providing bounds, cubature formulas, and numerical performance analysis.

Contribution

It presents a novel combined interpolation-regression method tailored for specific planar domains, with theoretical bounds and practical numerical validation.

Findings

Derived an upper bound for the operator.

Developed cubature formulas for weighted functions.

Numerical examples demonstrate method effectiveness.

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.