Counterexample

Is this true?

Increasing the number of equally spaced interpolation nodes improves the approximation

No — it is false.

The counterexample

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

Why it fails

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

Save for spaced revision (free account)

Keep practicing

Numerical convergence

A scheme assumed to converge, or to converge at its advertised rate.

Drill statements like this

Go deeper· Explained in full in Interpolation and numerical integration· Asked in CSIR NET June 2025· From Numerical Analysis › Interpolation and numerical integration with error terms

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsApp Telegram