Given a set of points ( , a common problem in numerical analysis is trying to estimate values of

On the face of it implementing this would seem to be a pretty trivial business, but doing so both accurately and efficiently is a surprisingly tricky affair, as we shall see in this post.

*x*,

_{i}*y*)

_{i}*y*for values of*x*that aren't in the set. The simplest scheme is linear interpolation, which connects points with consecutive values of*x*with straight lines and then uses them to calculate values of*y*for values of*x*that lie between those of their endpoints.On the face of it implementing this would seem to be a pretty trivial business, but doing so both accurately and efficiently is a surprisingly tricky affair, as we shall see in this post.

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