Mathematics, Numerical Analysis, Numerical Methods, Numerical Computation, Numerical Reasoning.
Δyᵢ = yᵢ₊₁ — yᵢ, for i = 0 to n-2 The second divided differences are calculated as: Δ²yᵢ = Δyᵢ₊₁ — Δyᵢ, for i = 0 to n-3 This process is continued until all divided differences are computed. The interpolating polynomial is then written as: P(x) = y₀ + Σ [ Δⁱy₀ * Π (x — xⱼ) ] for i = 0 to n-1