Numerical cubature and hyperinterpolation over Spherical Polygons
<|reference_start|>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 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.<|reference_end|>
@article{sommariva2024numerical,
    title={Numerical cubature and hyperinterpolation over Spherical Polygons},
    author={Alvise Sommariva},
    journal={arXiv preprint arXiv:2403.05733},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.05733},
    primaryClass={math.NA cs.NA}
}