Representing and analyzing scattered data on spheres (Q2737662)

In this interesting survey article, the authors discuss recent progress in the representation and analysis of scattered data on the unit sphere \(S^q\) of \(\mathbb{R}^{q+1}\). This research is mainly motivated by the representation and analysis of geophysical or meteorological data collected over the surface of the earth via satellites or ground stations. First, the interpolation and approximation of scattered data on \(S^q\) is discussed. These methods involve spherical basis functions. The analysis of scattered data on \(S^q\) is based on spherical wavelet schemes. Localization and uncertainty principles on \(S^q\) are discussed, too. A brief introduction to multilevel interpolation is given. In both the representation and analysis of scattered data on \(S^q\), efficient computations of Fourier coefficients and convolutions are needed. Therefore various numerical schemes are reviewed. The authors close by discussing quadrature methods, which arise in many of the spherical wavelet schemes as well as interpolation methods.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00017].