Iterated Interpolation: Neville's Method

   Unlike the Lagrange method, this method uses results of lower degree interpolation to compute higher degree results, making it more efficient. Each entry in the table is computed by the same formula:

   An example is shown below in table form:

The diagonal elements represent interpolation using the first 2, then 3, then 4...points in the table.

Consider the graph shown below to see how convergence could be made faster:

   To get the best two-point interpolation, the points nearest to x (here 3.25 and 3.5) should be on top of the table, followed by the next nearest point (3.0) for 3-point interpolation, etc.
   This can be done if we sort the table using |x-x_i| as the key.
   The resulting table is shown here: