Richardson Extrapolation Examples

Numerical Analysis · Axiom Academy

EXAMPLE Richardson Extrapolation Improve derivative accuracy by combining estimates from different step sizes Outstanding! You've used Richardson extrapolation to dramatically improve accuracy. Core Idea: Combine results from two step sizes to cancel leading error terms Formula for O(h²): D* = [4·D(h/2) - D(h)] / 3 gives O(h⁴) accuracy Error Improvement: From O(10⁻²) to O(10⁻⁵) - a 1000× improvement! Repeated Extrapolation: Can continue the process to achieve even higher accuracy Richardson extrapolation is a powerful general technique. It works for any method with known error order and is the basis for Romberg integration.

This is the written version of the interactive lesson above. See the full Numerical Analysis course.