Numerical cubature and hyperinterpolation over spherical polygons

The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we report the results about numerical cubature over spherical polygons P1, P2, approximating respectively the Australian and African continents. As an application we consider the reconstruction of functions over P1, also affected by perturbations, via hyperinterpolation and some of its variants. The open-source Matlab software used in the numerical tests is available at the author's homepage.