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5: Interpolation

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Consider the following problem: Given the values of a known function y=f(x) at a sequence of ordered points x0,x1,,xn, find f(x) for arbitrary x. When x0 xxn, the problem is called interpolation. When x<x0 or x>xn the problem is called extrapolation.

With yi=f(xi), the problem of interpolation is basically one of drawing a smooth curve through the known points (x0,y0),(x1,y1),,(xn,yn). This is not the same problem as drawing a smooth curve that approximates a set of data points that have experimental error. This latter problem is called least-squares approximation.

Here, we will consider three interpolation algorithms: (1) polynomial interpolation; (2) piecewise linear interpolation, and; (3) cubic spline interpolation.


This page titled 5: Interpolation is shared under a CC BY 1.0 license and was authored, remixed, and/or curated by Jeffrey R. Chasnov.

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