Peeking at different interpolation algorithms
08-02-2019, 09:27 PM (This post was last modified: 08-04-2019 01:43 PM by Albert Chan.)
Post: #2
 Albert Chan Senior Member Posts: 1,786 Joined: Jul 2018
RE: Peeking at different interpolation algorithms
With divided difference, there is no requirement that the table be sorted.
Just do Forward Divided Difference, with the entries closest to interested region up on top.

Example, from https://jp.mathworks.com/matlabcentral/f...on-formula
(note: the link had the entries entered wrong, below is corrected points)

Points: (-2, 18.4708), (-1, 17.8144), (0, 17.107), (1, 16.3432), (2, 15.5154), find y(0.25):

Assume calculations with 6 sig. digits, and we want best interpolated values in the middle:

Code:
p   y(p)      Divided Difference Table +0  17.107 +1  16.3432  -0.763800 -1  17.8144  -0.735600  -0.0282000 +2  15.5154  -0.766333  -0.0307330  -0.00126650 -2  18.4708  -0.738850  -0.0274830  -0.00108333  -0.0000915850

y(p) = 17.107 + (p-0)*(-0.7638 + (p-1)*(-0.0282 + (p+1)*(-0.0012665 + (p-2)*(-0.000091585))))

→ y(0.25) ≈ 16.9216

Above formula is same (except slight rounding errors) as Gauss Forward Formula:
Code:
p   y(p)      Difference Table -2  18.4708   -1  17.8144  -0.6564 +0  17.107   -0.7074  -0.0510 +1  16.3432  -0.7638  -0.0564  -0.0054 +2  15.5154  -0.8278  -0.0640  -0.0076  -0.0022

y(p) = $$17.107 + \binom{p}{1}(-0.7638) + \binom{p}{2}(-0.0564) + \binom{p+1}{3}(-0.0076) + \binom{p+1}{4}(-0.0022)$$
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 Messages In This Thread Peeking at different interpolation algorithms - Namir - 10-21-2017, 03:00 PM RE: Peeking at different interpolation algorithms - Albert Chan - 08-02-2019 09:27 PM RE: Peeking at different interpolation algorithms - Albert Chan - 08-10-2019, 08:49 PM RE: Peeking at different interpolation algorithms - Albert Chan - 08-04-2019, 01:28 PM

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