26.10 INTERPOLATION WITH UNEQUAL SPACED POINTS

The classical polynomial interpolating formulae discussed so far are limited to the case in which intervals of independent variables were equally spaced. We shall now discuss interpolation formulae with unequally spaced values of the argument.

(a) Divided Differences

Let f (x0), f (x1),…, f (xn) be the values of a function f corresponding to the arguments x0, x1,‥, xn, where the intervals x1– x0, x2–x1,…, xn– xn–1 are not necessarily equally spaced. Then the first divided differences of f for the arguments x0, x1, x2,… are defined by

 

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and so on. The second divided difference (divided difference ...

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