Multidimensional Spline Interpolation: Theory and Applications
| Autor: | Christian Habermann, Fabian Kindermann |
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| Rok vydání: | 2007 |
| Předmět: |
Economics
Econometrics and Finance (miscellaneous) Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Monotone cubic interpolation Bilinear interpolation Linear interpolation Mathematics::Numerical Analysis Computer Science Applications Polynomial interpolation Nearest-neighbor interpolation ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Applied mathematics Bicubic interpolation Spline interpolation ComputingMethodologies_COMPUTERGRAPHICS Interpolation Mathematics |
| Zdroj: | Computational Economics. 30:153-169 |
| ISSN: | 1572-9974 0927-7099 |
| DOI: | 10.1007/s10614-007-9092-4 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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