Report Number: CS-TR-79-719
Institution: Stanford University, Department of Computer Science
Title: Extrapolation of asymptotic expansions by a modified Aitken $\delta^2$-formula
Author: Bjorstad, Petter
Author: Dahlquist, Germund
Author: Grosse, Eric H.
Date: March 1979
Abstract: A modified Aitken formula permits iterated extrapolations to efficiently estimate $s_\infty$ from $s_n$ when an asymptotic expansion $s_n = s_\infty + n^{-k} (c_0 + c_1 n^{-1} + c_2 n^{-2} + ... )$ holds for some (unknown) coefficients $c_j$. We study the truncation and irregular error and compare the method with other forms of extrapolation.