Spherical Scattered Data Quasi-interpolation by Gaussian Radial Basis Function

Since the spherical Gaussian radial function is strictly positive definite, theauthors use the linear combinations of translations of the Gaussian kernel to interpolatethe scattered data on spheres in this article. Seeing that target functions are usually outsidethe native spaces, and that one has to solve a large scaled system of linear equations toobtain combinatorial coefficients of interpolant functions, the authors first probe into someproblems about interpolation with Gaussian radial functions. Then they construct quasiinterpolationoperators by Gaussian radial function, and get the degrees of approximation.Moreover, they show the error relations between quasi-interpolation and interpolation whenthey have the same basis functions. Finally, the authors discuss the construction andapproximation of the quasi-interpolant with a local support function.