The use of normalized binomial coefficients as weights to accelerate convergence of oscillatory first‐order iterations

Document Type


Publication Date



Department of Chemistry; Department of Chemical Engineering


Normalized binomial coefficients can be used as weights in averaging the members of a sequence of iterates resulting from an oscillatory process of first order, to obtain an improved estimate of the fixed point of the process. This procedure results in convergence whether the original oscillatory first‐order process is convergent or divergent, but not too rapidly divergent. By way of example, this method causes the omega technique to converge much more rapidly and results in convergence even when the sequence obtained by the unmodified omega technique diverges. Normalized‐binomial‐coefficient‐weighted averaging of three successive iterates, though appreciably simpler, is a close approximation to Aitken's δ2 process in cases of oscillatory iterations, and is profitably used in place of the latter process, especially in algebraic developments.

Publisher's Statement

Copyright © 1967 John Wiley & Sons, Inc. Publisher’s version of record:

Publication Title

International Journal of Quantum Chemistry