Interpolating and Extrapolating
Interpolating is not always a good idea and one should be especially careful when extrapolating. These operations are nevertheless sometimes very useful. Classical methods are described for the univariate and multivariate case. Conditions that make very high-degree polynomial interpolation a viable option are explained. Pros and cons of rational interpolation are presented. Richardson’s extrapolation principle is described. It is used, for instance, in numerical integration and differentiation as well as for solving differential equations. Kriging, a multivariate interpolation method initially developed in the context of mining, receives special attention. It is increasingly used in computer experiments to build surrogate models for functions that are very costly to evaluate.
KeywordsInput Factor Polynomial Interpolation Interpolation Point Vandermonde Matrix Rational Interpolation
- 9.de Boor, C.: A Practical Guide to Splines, revised edn. Springer, New York (2001)Google Scholar
- 12.Cressie, N.: Statistics for Spatial Data. Wiley, New York (1993)Google Scholar
- 13.Krige, D.: A statistical approach to some basic mine valuation problems on the Witwatersrand. J. Chem. Metall. Min. Soc. 52, 119–139 (1951)Google Scholar
- 16.Vazquez, E., Walter, E.: Estimating derivatives and integrals with Kriging. In: Proceedings of 44th IEEE Conference on Decision and Control (CDC) and European Control Conference (ECC), pp. 8156–8161. Seville, Spain (2005)Google Scholar