Runge’s phenomenon and Chebyshev nodes

Why node placement matters: equally spaced interpolation nodes can make the error diverge as the polynomial degree grows (Runge’s 1901 example), while Chebyshev nodes keep the error shrinking.

Runge’s phenomenon: equally spaced interpolation diverges

Runge's phenomenon: equally spaced interpolation diverges

Chebyshev nodes: the cure for Runge’s phenomenon

Chebyshev nodes: the cure for Runge's phenomenon