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

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.

Source: arXiv:2604.24748v1 - http://arxiv.org/abs/2604.24748v1 PDF: https://arxiv.org/pdf/2604.24748v1 Original Link: http://arxiv.org/abs/2604.24748v1