A mixed interpolation-regression method for numerical integration on some planar domains
This is an incremental contribution for researchers in numerical analysis seeking improved integration methods on specific planar domains.
The paper introduces a mixed interpolation-regression operator for numerical integration on planar domains like ellipses, annuli, and polygons, deriving an upper bound and testing cubature formulas with numerical examples.
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.