A Rational Interpolation Scheme with Superpolynomial Rate of Convergence
The purpose of this study is to construct a high-order interpolation scheme for arbitrary scattered datasets. The resulting function approximation is an interpolation function when the dataset is exact, or a regression if measurement errors are present. We represent each datapoint with a Taylor seri...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Society for Industrial and Applied Mathematics,
2010-08-17T14:12:59Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | The purpose of this study is to construct a high-order interpolation scheme for arbitrary scattered datasets. The resulting function approximation is an interpolation function when the dataset is exact, or a regression if measurement errors are present. We represent each datapoint with a Taylor series, and the approximation error as a combination of the derivatives of the target function. A weighted sum of the square of the coefficient of each derivative term in the approximation error is minimized to obtain the interpolation approximation. The resulting approximation function is a high-order rational function with no poles. When measurement errors are absent, the interpolation approximation converges to the target function faster than any polynomial rate of convergence. |
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