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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Behforooz G.H., Papamichael N. (1979). End conditions for cubic spline interpolation. IMA Journal of Applied Mathematics 23, 355–366
de Boor C. (1978). A practical guide to Splines. New York, Springer
Epstein L.G., Zin S.E. (1991). Substitution, risk aversion, and the temporal behavior of consumption and asset returns: An empirical analysis. Journal of Political Economy 99, 263–286
Fehr, H., & Habermann, Ch. (2005). Risk sharing and efficiency implications of progressive pension arrangements. CESifo Working Paper No. 1568, München.
Heer B., Maussner A. (2005). Dynamic general equilibrium modelling. Berlin, Springer
İmrohoroğlu A., İmrohoroğlu S., Joines D.H. (1995). A life cycle analysis of social security. Economic Theory 6(1): 83–114
Judd K.L. (1998). Numerical methods in economics. Massachusetts, The MIT Press
Miranda M.J., Fackler P.L. (2002). Applied computational economics and finance. Massachusetts, The MIT Press
Nishiyama S., Smetters K. (2005). Consumption taxes and economic efficiency with idiosyncratic wage shocks. Journal of Political Economy 113, 1088–1115
Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. (2002). Numerical recipes in C. Cambridge, Cambridge University Press
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Habermann, C., Kindermann, F. Multidimensional Spline Interpolation: Theory and Applications. Comput Econ 30, 153–169 (2007). https://doi.org/10.1007/s10614-007-9092-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10614-007-9092-4