A classical and well-studied problem in numerical analysis is to find a continuous function that interpolates a discrete set of data points. Most of the theory on this subject assumes that the exact position of each interpolation node is known with certainty, an assumption that is unlikely to hold in scientific practice. This paper analyzes the effects of measurement errors on interpolating functions and provides methods for constructing prediction intervals based upon the distributions of those errors.
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Ethan Wilson (2025) studied this question.
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