Interpolation

For thoughtful child sponsors

In mathematics, interpolation is used to approximate a function for which we only know values for a discrete set of values of the independent variable. For example, suppose we have a table like

x   f(x)

-   ----

1     1

2     4

3     9

4    16

5 25

We immediately recognize that f(x) can be fit precisely by the function x² but in general this is not the case when we want to interpolate. Suppose we would like the value of f(x) which corresponds to x = 1.7. The simplest method is linear interpolation between the values for x = 1 and x = 2:

Of course, if the underlying function is really x² the true solution is

Thus interpolation is usually not exact. Special care must be taken to avoid extrapolation unless one knows very well what one is doing.