Multivariate hermite interpolation in euclidean space and its unit sphere by radial basis functions

In this thesis, we consider radial basis function interpolations in d-dimensional Euclidean space Hd and the unit sphere 5d_1, where the data is generated not only by point-evaluations, but also by the derivatives, or differential/pseudo-differential operators. Some sufficient and necessary conditions for the well-posedness of the interpolations are given. The results on sensitivity and sta bility of the interpolation systems are obtained. The optimal properties of the interpolants are analysed through the variational framework and reproducing kernel Hilbert space property, the error bounds and convergence rates of the interpolants are derived. The admissible reproducing kernel Hilbert spaces are also characterised.