Optimal Multivariate Interpolation

Abstract

In this chapter, we are concerned with the problem of multivariate data interpolation. The main focus lies on the concept of minimizing a quadratic form which, in practice, emerges from a physical model, subject to the interpolation constraints. The approach is a natural extension of the one-dimensional polynomial spline interpolation. Besides giving a basic outline of the mathematical framework, we design a fast numerical scheme and analyze the performance quality. We finally show that optimal interpolation is closely related to standard linear stochastic estimation methods.