Estimation of convergence orders in repeated richardson extrapolation

Abstract

LetA(h) be an approximation depending on a single parameterh to a fixed quantityA, and assume thatA−A(h)=c ₁ h k ₁ +c ₂ h ^k ₂ +.... Given a sequence ofh-valuesh ₁>h ₂>...>h _n and corresponding computed approximationsA(h _i ), the orders for repeated Richardson extrapolation are estimated, and the repeated extrapolation is performed. Hence in this case the algorithm described here can do the same work as Brezinski'sE-algorithm and at the same time provide a check whether repeated extrapolation is justified.