On the approximation order and numerical stability of local lagrange interpolation by polyharmonic splines

This paper proves convergence rates for local scattered data interpolation by polyharmonic splines. To this end, it is shown that the Lagrange basis functions of polyharmonic spline interpolation are invariant under uniform scalings. Consequences of this important result for the numerical stability of the local interpolation scheme are discussed. A stable algorithm for the evaluation of polyharmonic spline interpolants is proposed.