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.

http://i.stanford.edu/pub/cstr/reports/cs/tr/79/719/CS-TR-79-719.pdf