Abstract
Consider a family of functions of a single variable x,
having n + 1 parameters αo, ..., αn whose values characterize the individual functions in this family. The interpolation problem for Φ consists of determining these parameters ai so that for n + 1 given real or complex pairs of numbers (xi, fi), i=0, ..., n, with xi ≠ xk for i ≠ k,
holds. We will call the pairs (x i, f i) support points, the locations x i support abscissas, and the values f i support ordinates. Occasionally, the values of derivatives of Φ are also prescribed.
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Stoer, J., Bulirsch, R. (1993). Interpolation. In: Introduction to Numerical Analysis. Texts in Applied Mathematics, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-2272-7_2
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