Peeking at different interpolation algorithms
08-04-2019, 01:28 PM (This post was last modified: 08-04-2019 01:44 PM by Albert Chan.)
Post: #3
 Albert Chan Senior Member Posts: 1,896 Joined: Jul 2018
RE: Peeking at different interpolation algorithms
Perhaps an easier way to produce Forward Divided Difference polynomial:

New Formulas and Methods for Interpolation, Numerical Differentiation and Numerical Integration

Redoing post #2 with the New Divided Difference Table, again assume 6 sig. digits calculations

Code:
p   y(p)      New Divided Difference Table +0  17.107 +1  16.3432  -0.7638 -1  17.8144  -0.7074  -0.0282 +2  15.5154  -0.7958  -0.032   -0.00126667 -2  18.4708  -0.6819  -0.0273  -0.0009     -0.0000916675

Top entries are "locked", and use to compute the slope (divided difference).

1st column = [ (y-17.107) / (x-0) for (x,y) in [[1,16.3432],[-1,17.8144],[2,15.5154],[-2,18.4708]]]
2nd colume = [ (y+0.7638)/(x-1) for (x,y) in [[-1,-0.7074],[2,-0.7958],[-2,-0.6819]]]
...

y(p) = 17.107 + (p-0)*(-0.7638 + (p-1)*(-0.0282 + (p+1)*(-0.00126667 + (p-2)*(-0.0000916675))))

This interpolation scheme were used by Acton Forman's Numerical Method that Work.
The book were originally published in 1970, so perhaps above is not that "New"