Polynomial Interpolation on the Unit Sphere

On Polynomial Interpolation on the Unit Ball

Polynomial interpolation on the unit ball of R d has a unique solution if the points are located on several spheres inside the ball and the points on each sphere solves the corresponding interpolation problem on the sphere. Furthermore, the solution can be computed in a recursive way.

MEAN VALUE INTERPOLATION ON SPHERES

In this paper we consider   multivariate Lagrange mean-value interpolation problem, where interpolation parameters are integrals over spheres. We have   concentric spheres. Indeed, we consider the problem in three variables when it is not correct.  

Polynomial interpolation on the unit sphere II

The problem of interpolation at (n+1) points on the unit sphere S by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials.

Polynomial Interpolation on the Unit Sphere and on the Unit Ball

Analysis on the Unit Ball and on the Simplex

Many results on the unit ball and those on the simplex can be deduced from each other or from the corresponding results on the unit sphere. The areas in which such a connection appears include orthogonal polynomials, approximation, cubature formulas and polynomial interpolation. We explain this phenomenon in some detail.