The bookUnit 3 · Numerical Analysis62 / 83

Interpolation and numerical integration with error terms

Why this is asked: Degree of precision is the key number: trapezoidal 1, Simpson 3, n-point Gauss 2n−1. Interpolation error carries f⁽ⁿ⁺¹⁾/(n+1)! times the node product.

Interpolation and numerical integration

The written notes for this page come with the Notes pack. The video, the visual and the practice below are free.

See pricing

See it move

Degree of exactness, and why more nodes can be worseinteractive

Trapezium versus Simpson, and Runge's phenomenon in one example.

Unlock interactive visuals

The trap here

“Increasing the number of equally spaced interpolation nodes improves the approximation” — false

Runge's function $1/(1 + 25x^{2})$ on [−1, 1]

The interpolants diverge near the endpoints as $n \to \infty$ . Chebyshev nodes restore convergence.