Hyperinterpolation for Spectral Wave Propagation Models in Three Dimensions

Numerical hyperinterpolation over spherical triangles

“…Sloan in 1995 [17] and initially used mainly on the whole sphere [13], hyperinterpolation is essentially an orthogonal (Fourier-like) projection on polynomial spaces, with respect to the discrete measure associated with a positive algebraic quadrature formula, or in other words a weighted least-squares polynomial approximation at the quadrature nodes. In the last twenty years the subject has been developed and extended to several 2-dimensional and 3-dimensional domains, such as cubes and balls but also less standard ones, from both the theoretical and the modelling/computational point of view; cf., e.g., [6,11,12,5,18,21,22] with the references therein.…”