(12C Platinum) Sums of Powers of N numbers

[Albert Chan]

(01-23-2019 05:40 PM)Albert Chan Wrote:  

Code:

N Sum Interpolation for N=10
4 100
3 36  484
2 9   373  1261
1 1   298  1135  2269
0 0   250  1030  2185  3025

Just discovered every interpolation numbers have meanings.

Example, 4th line:
(10, 298) = linear fit of 2 points: (4,100), (1,1)
(10, 1135) = quadratic fit of 3 points: (4,100), (3,36), (1,1)
(10, 2269) = cubic fit of 4 points: (4,100), (3,36), (2,9), (1,1)

Since data points is sorted (closest to N=10 on top), diagonal numbers were "best" estimates.

Another trick: with quadratic regression, above only need 4 interpolations.