The rational iteration method by Georges Lemaitre (working papers)

TL;DR

This paper explores Georges Lemaitre's 1942 'rational iteration' method, which rediscovered classical acceleration techniques like Aitken's process and Steffensen's method, linking them to his scientific work on differential equations.

Contribution

It reveals the historical and mathematical context of Lemaitre's 1942 method, connecting it to modern acceleration techniques and his research interests.

Findings

Lemaitre's method rediscovered Aitken's process and Steffensen's method.

The method was motivated by solving differential equations.

Historical analysis of Lemaitre's scientific concerns.

Abstract

In 1942, the famous astronomer and physicist Belgian Georges Lemaitre (1894-1966) published in the Bulletin of the class of Sciences of the Royal Academy of Belgium, an article in which he proposes a method that he calls "rational iteration". He rediscovers both the $\Delta^{2}$ Aitken process and the Steffensen's method. We will see how the scientific concerns of Georges Lemaitre in the year 1942 (resolutions of differential equations) have led to this rediscovery.