Click to add sample points — Newton's divided difference polynomial grows term by term
Newton's divided difference formula: P(x) = f[x₀] + f[x₀,x₁](x−x₀) + f[x₀,x₁,x₂](x−x₀)(x−x₁) + … Each new point adds exactly one term. The Runge phenomenon shows that equally-spaced nodes can cause oscillation near the edges — Chebyshev nodes avoid this.