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 a spherical polygon $\cal P$ approximating Australia and reconstruction of functions over such $\cal P$, 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.

翻译：本文旨在提出一种策略，用于确定球面多边形上具有低基数正求积公式的节点和权重，该公式对给定次数的多项式几乎精确。在数值实验部分，我们报告了关于逼近澳大利亚的球面多边形$\cal P$上的数值求积结果，以及通过超插值及其变体在该多边形$\cal P$上（包括受扰动影响的情况）进行函数重建的结果。数值测试中使用的开源Matlab软件可在作者主页获取。