Interpolation

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 fitted 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 following formula demonstrates how we would interpolate (linearly) between the values for X = 1 and X = 2.

• f(1.7) = f(1) + [(1.7-1)/(2-1)]*(f(2)-f(1)) = 1 + 0.7*(4-1) = 1 + .7*3 = 3.1

Also see [polynomial interpolation]?.