Newton's Divided Difference Calculator
Build Newton's interpolating polynomial using the divided difference table method.
Data Points
0:
1:
2:
3:
P(2.5)
15.6250000000
Divided Difference Table
| x | f[·] | f[·,·] | f[·,·,·] | ... |
|---|---|---|---|---|
| 1 | 1.0000 | 7.0000 | 6.0000 | 1.0000 |
| 2 | 8.0000 | 19.0000 | 9.0000 | |
| 3 | 27.0000 | 37.0000 | ||
| 4 | 64.0000 |
Coefficients (first row): [1.0000, 7.0000, 6.0000, 1.0000]
Newton Form
P(x) = 1.0000 + 7.0000(x-1) + 6.0000(x-1)(x-2) + 1.0000(x-1)(x-2)(x-3)
Verification
P(1)=1.00 ✓P(2)=8.00 ✓P(3)=27.00 ✓P(4)=64.00 ✓
Newton's Divided Differences
Formula
f[xᵢ,...,xⱼ] = (f[xᵢ₊₁,...,xⱼ] - f[xᵢ,...,xⱼ₋₁]) / (xⱼ - xᵢ)
Advantages
- Easy to add new points
- Efficient computation
- Natural error estimation