Solvability of multivariate interpolation by radial or related function

In this paper, we consider multivariate interpolation with radial basis functions of finite smoothness. In particular, we show that interpolants by radial basis functions in ^d with finite smoothness of even order converge to a polyharmonic spline ...

In this study, we are mainly interested in error estimates of interpolation, using smooth radial basis functions such as multiquadrics. The current theories of radial basis function interpolation provide optimal error bounds when the basis function $\phi$ ...