Newton's interpolation: P(x) = f[x₀] + f[x₀,x₁](x−x₀) + f[x₀,x₁,x₂](x−x₀)(x−x₁) + ... Divided differences: f[xᵢ,xⱼ] = (f[xⱼ]−f[xᵢ])/(xⱼ−xᵢ). Forward: uses Δ operator. Backward: uses ∇ operator.
How to Use
Enter data points:
- Points: (x₀,y₀), (x₁,y₁), ...
- Evaluate at: x value
- Output: P(x) + diff table
vs Lagrange
Newton's form allows adding points without recomputing everything. New point = one more divided difference + one more term. Lagrange requires complete recalculation.
Forward vs Backward
Forward: best near x₀ (beginning). Backward: best near xₙ (end). Both give the same polynomial but different computational forms.
Step-by-Step Instructions
- 1Enter data points.
- 2View divided differences.
- 3See polynomial.
- 4Enter x to evaluate.
- 5Get interpolated value.