Sequential Barycentric Interpolation
Polynomial interpolators may exhibit oscillating behaviour which often makes them inadequate for modelling functions. A well-known correction to this problem is to use Chebyshev design points. However, in a sequential strategy it is not very clear how to add points, while still improving polynomial interpolation. We present a sequential design alternative by allocating an extra observation where the difference between consecutive interpolators is largest. Our proposal is independent of the response and does not require distributional assumptions. In simulated examples, we show the good interpolation performance of our proposal and its asymptotical convergence to the Chebyshev distribution.
KeywordsDesign Point Design Region Large Sample Property Chebyshev Point Sequential Interpolation
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