This paper considers extremal systems of points on the unit sphere Sr Rr+1, related problems of numerical integration and geometrical properties of extremal systems. Extremal sys...
(A) The celebrated Gaussian quadrature formula on finite intervals tells us that the Gauss nodes are the zeros of the unique solution of an extremal problem. We announce recent re...
A set XN of N points on the unit sphere is a spherical t-design if the average value of any polynomial of degree at most t over XN is equal to the average value of the polynomial o...
Congpei An, Xiaojun Chen, Ian H. Sloan, Robert S. ...
Numerical methods for solving the systems of partial differential equations arising in geophysical fluid dynamics rely on a variety of spatial discretization schemes (e.g. finit...
In this paper we analyse a hybrid approximation of functions on the sphere S2 R3 by radial basis functions combined with polynomials, with the radial basis functions assumed to be...