Lagrangian Interpolation

[Albert Chan]

Hi, Thomas Klemm

Your way works too, but I prefer Acton's Forman style.
I like to do row-by-row, and this lined up numbers to use.


Acton Forman style

Code:

        f    D          D^2      D^3
  1     1   
  2     8   7/1=7
  5   125   124/4=31    24/3=8
  7   343   342/6=57    50/5=10  2/2=1

Conventional Divided Difference, we need to trace the diagonal for x's to use.

Code:

        f    D          D^2      D^3
  1     1
            7/1=7
  2     8               32/4=8
            117/3=39             6/6=1
  5   125               70/5=14
            218/2=109
  7   343

Both ways get the same [1,7,8,1] digaonal

f = 1 + (x-1)*(7 + (x-2)*(8 + (x-5)*1)) = x^3