Martin J. Gander - Landmarks in the History of Iterative Methods for Linear Systems

Nous aurons l'occasion d'écouter une présentation de Martin J. Gander (Université de Genève) intitulée Landmarks in the History of Iterative Methods for Linear Systems, le 09 septembre 2025 à l'ENSTA Paris en Amphi 2234. 

Résumé :
Iterative methods for linear systems were invented for the same reasons as they are used today, namely to reduce computational cost. Gauss states in a letter to his friend Gerling in 1823: "you will in the future hardly eliminate directly, at least not when you have more than two unknowns". 
After a historical introduction to such classical stationary iterative methods, I will explain how the idea of extrapolation leads to Krylov methods, which are in fact not solvers but convergence accelerators. 
I will then introduce modern iterative methods for solving partial differential equations, which come in two main classes: domain decomposition methods and multigrid methods. These methods develop their full potential when used together with Krylov methods, namely as preconditioners. 
Reference: Landmarks in the History of Iterative Methods, Martin J. Gander, Philippe Henry and Gerhard Wanner, SIAM Review, 2025