Preconditioning techniques based on the Birkhoff–von Neumann decomposition

Michele Benzi (1) , Alex Pothen (2) , Bora Uçar (3, 4)

1 Department of Mathematics and Computer Science [Emory University]
2 Department of Computer Science [Purdue]
3 LIP - Laboratoire de l'Informatique du Parallélisme
4 ROMA - Optimisation des ressources : modèles, algorithmes et ordonnancement

We introduce a class of preconditioners for general sparse matrices based on the Birkhoff-von Neumann decomposition of doubly stochastic matrices. These precondi- tioners are aimed primarily at solving challenging linear systems with highly unstructured and indefinite coefficient matrices. We present some theoretical results and numerical experiments on linear systems from a variety of applications.

Domaines: Mathématique discrète [cs.DM]; Algorithme et structure de données [cs.DS]; Analyse numérique [math.NA]; Combinatoire [math.CO]

Michele Benzi, Alex Pothen, Bora Uçar. Preconditioning techniques based on the Birkhoff–von Neumann decomposition. [Research Report] RR-8914, Inria - Research Centre Grenoble – Rhône-Alpes. 2016. ⟨hal-01318486v2⟩