Computational Economics

, Volume 30, Issue 2, pp 153–169 | Cite as

Multidimensional Spline Interpolation: Theory and Applications

Article

Abstract

Computing numerical solutions of household’s optimization, one often faces the problem of interpolating functions. As linear interpolation is not very good in fitting functions, various alternatives like polynomial interpolation, Chebyshev polynomials or splines were introduced. Cubic splines are much more flexible than polynomials, since the former are only twice continuously differentiable on the interpolation interval. In this paper, we present a fast algorithm for cubic spline interpolation, which is based on the precondition of equidistant interpolation nodes. Our approach is faster and easier to implement than the often applied B-Spline approach. Furthermore, we will show how to loosen the precondition of equidistant points with strictly monotone, continuous one-to-one mappings. Finally, we present a straightforward generalization to multidimensional cubic spline interpolation.

Keywords

Interpolation Multidimensional cubic splines 

JEL Classification

C63 C65 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of WürzburgWürzburgGermany

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