Richardson Extrapolation

Numerical Analysis · Axiom Academy

LESSON Richardson Extrapolation Getting more accuracy from less-accurate approximations Suppose we have an approximation A(h) with error O(h²): If we compute A(h/2), using half the step size: Since we know the error structure, we can eliminate the a₁h² term! To eliminate the O(h²) term, multiply A(h/2) by 4 and subtract A(h): Let's compute f'(1) for f(x) = sin(x) using central differences and Richardson extrapolation: 4 General Richardson Extrapolation The formula depends on the error order of the original method: 5 Repeated Extrapolation: The Tableau We can apply Richardson extrapolation repeatedly to get even higher accuracy: Each column improves the order by 2: O(h²) → O(h⁴) → O(h⁶) → ...

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