Numerical analysis
Bounding stability constants for affinely parameter-dependent operators
Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1236-1240.

In this article we introduce new possibilities of bounding the stability constants that play a vital role in the reduced basis method. By bounding stability constants over a neighborhood we make it possible to guarantee stability at more than a finite number of points and to do that in the offline stage. We additionally show that Lyapunov stability of dynamical systems can be handled in the same framework.

Nous présentons de nouvelles méthodes pour borner les constantes de stabilité qui jouent un rôle essentiel dans les approximations par bases réduites. Notre méthode nous permet de borner les constantes dans tout un voisinage et non seulement en un nombre fini de points. Nous montrons aussi qu'on peut démontrer la stabilité de Liapounov dans le même cadre.

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DOI: 10.1016/j.crma.2016.10.003
O'Connor, Robert 1

1 RWTH Aachen University, Aachen, Germany
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O'Connor, Robert. Bounding stability constants for affinely parameter-dependent operators. Comptes Rendus. Mathématique, Volume 354 (2016) no. 12, pp. 1236-1240. doi : 10.1016/j.crma.2016.10.003. http://www.numdam.org/articles/10.1016/j.crma.2016.10.003/

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