# The rational iteration method by Georges Lemaître

The rational iteration method by Georges Lemaître Numer Algor https://doi.org/10.1007/s11075-018-0551-x ORIGINAL PAPER Herve ´ Le Ferrand Received: 14 April 2018 / Accepted: 15 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We explain in this article how the famous Belgian astronomer and physi- cist Georges Lemaˆ ıtre, a specialist in the theory of relativity, rediscovered, during the Second World War from Gauss’ work, Aitken’s Δ process. He called his dis- covery the rational iteration method and used it to solve an ordinary differential equation. After giving some historical elements on Aitken’s Δ process and Stef- fensen’s method, we examine in detail the genesis of the rational iteration, and then its application by Lemaˆ ıtre to Picard’s iterates to solve the differential equation y = dy/dx = 2y (y − x). Keywords Lemaˆ ıtre · Aitken · Steffensen · Δ process · Fixed point · Ordinary differential equation · Picard iterative process Mathematics Subject Classification (2010) 65B05 · 65H05 · 65L05 1 Introduction Nowadays, the Belgian astronomer and physicist Georges Lemaˆ ıtre (1894–1966) is considered as one of the fathers of the Big Bang theory [19, 22]. In 1942, he pub- lishedinthe Bulletin de la Classe des Sciences de l’Academie ´ Royale http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Numerical Algorithms Springer Journals

# The rational iteration method by Georges Lemaître

, Volume OnlineFirst – May 28, 2018
17 pages

/lp/springer_journal/the-rational-iteration-method-by-georges-lema-tre-n1fQ2aV553
Publisher
Springer Journals
Subject
Computer Science; Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis
ISSN
1017-1398
eISSN
1572-9265
D.O.I.
10.1007/s11075-018-0551-x
Publisher site
See Article on Publisher Site

### Abstract

Numer Algor https://doi.org/10.1007/s11075-018-0551-x ORIGINAL PAPER Herve ´ Le Ferrand Received: 14 April 2018 / Accepted: 15 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We explain in this article how the famous Belgian astronomer and physi- cist Georges Lemaˆ ıtre, a specialist in the theory of relativity, rediscovered, during the Second World War from Gauss’ work, Aitken’s Δ process. He called his dis- covery the rational iteration method and used it to solve an ordinary differential equation. After giving some historical elements on Aitken’s Δ process and Stef- fensen’s method, we examine in detail the genesis of the rational iteration, and then its application by Lemaˆ ıtre to Picard’s iterates to solve the differential equation y = dy/dx = 2y (y − x). Keywords Lemaˆ ıtre · Aitken · Steffensen · Δ process · Fixed point · Ordinary differential equation · Picard iterative process Mathematics Subject Classification (2010) 65B05 · 65H05 · 65L05 1 Introduction Nowadays, the Belgian astronomer and physicist Georges Lemaˆ ıtre (1894–1966) is considered as one of the fathers of the Big Bang theory [19, 22]. In 1942, he pub- lishedinthe Bulletin de la Classe des Sciences de l’Academie ´ Royale

### Journal

Numerical AlgorithmsSpringer Journals

Published: May 28, 2018

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