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 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:

<math>f(1.7)=f(1)+\frac{1.7-1}{2-1}(f(2)-f(1))=1+0.7(4-1)=1+0.7\cdot 3=3.1.</math>

See also:

• Polynomial interpolation
• Spline interpolation[?]
• Bilinear interpolation[?]
• Curve fitting[?]
• Pareto interpolation