We introduce a class of preconditioners for general sparse matrices based on the Birkhoff–von Neumann decomposition of doubly stochastic matrices. These preconditioners 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.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1418889
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: SOLHAR (ANR-13-MONU-0007)
Funding statement: The work of Michele Benzi was supported in part by NSF grant DMS-1418889. Bora Uçar was supported in part by French National Research Agency (ANR) project SOLHAR (ANR-13-MONU-0007).
We thank Alex Pothen for his contributions to this work. This work resulted from the collaborative environment offered by the Dagstuhl Seminar 14461 on High-Performance Graph Algorithms and Applications in Computational Science (November 9–14, 2014).
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