Math

Interpolation and Runge's phenomenon

Compare polynomial and cubic-spline interpolation, expose Runge’s phenomenon and measure the effect of Chebyshev nodes.

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Increase the node count to expose Runge oscillations near the ends. Compare barycentric polynomial interpolation and a natural cubic spline. Errors are sampled at 2001 points; the plot clips extreme overshoot to keep the function readable.

Equations used in the module

Equations
p(x) = [Σ wᵢ yᵢ/(x−xᵢ)] / [Σ wᵢ/(x−xᵢ)]
wᵢ = 1 / ∏ⱼ≠ᵢ(xᵢ−xⱼ)
Chebyshev–Lobatto: xᵢ = −cos(πi/(n−1))
Natural cubic spline: continuous first and second derivatives; s″(−1)=s″(1)=0

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