(12C Platinum) Sums of Powers of N numbers

[Albert Chan]

Hi, Thomas Klemm

The trick is from Acton Forman's book Numerical Method that Work, p94
It was a modified Aitken's method.

First, arrange the points in sorted order, closest to interpolated N on top.
Back in the old days, people don't have computers readily available.
The sorting ensured for each columns, interpolated values "tighter".
Manual calculation mistakes are thus easier to spot.

For each column, top point is "locked", and do interpolation with other points.

First column:
(4,100) and (3,36) => (10,484)
(4,100) and (2,9) => (10,373) ...
Second column:
(3,484) and (2,373) => (10,1261)
(3,484) and (1,298) => (10,1135) ...
...
Last column: (1,2269) and (0,2185) => (10,3025)

Without sorting, we still get the same interpolated value, but mistakes harder to spot.

Code:

N Sum Interpolation for N=10
0 0   
1 1   10
2 9   45  325
3 36  120 505 1765
4 100 250 730 1945 3025