Error estimates for Hermite interpolation on spheres

Error estimates for scattered data interpolation on spheres

We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our approach partly follows the general theory of Golomb and Weinberger and related estimates. These error estimates are then based on series expansions of smooth functions in terms of spherical harmonics....

Error bounds for bivariate piecewise hermite interpolation

Hermite interpolation with radial basis functions on spheres

We show how conditionally negative deenite functions on spheres coupled with strictly completely monotone functions (or functions whose derivative is strictly completely monotone) can be used for Hermite interpolation. The classes of functions thus obtained have the advantage over the strictly positive deenite functions studied in 17] that closed form representations (as opposed to series expan...

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.  

Error estimates for generalized barycentric interpolation

We prove the optimal convergence estimate for first order interpolants used in finite element methods based on three major approaches for generalizing barycentric interpolation functions to convex planar polygonal domains. The Wachspress approach explicitly constructs rational functions, the Sibson approach uses Voronoi diagrams on the vertices of the polygon to define the functions, and the Ha...