Preconditioning Techniques Based on the Birkhoff–von Neumann Decomposition
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Michele Benzi
und
Bora Uçar
Abstract
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).
Acknowledgements
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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© 2017 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- On the Efficiency of a Family of Steffensen-Like Methods with Frozen Divided Differences
- Preconditioning Techniques Based on the Birkhoff–von Neumann Decomposition
- A Priori and A Posteriori Estimates of Conforming and Mixed FEM for a Kirchhoff Equation of Elliptic Type
- A Time-Stepping DPG Scheme for the Heat Equation
- Hybrid Spectral Difference Methods for an Elliptic Equation
- Simplified Iterated Lavrentiev Regularization for Nonlinear Ill-Posed Monotone Operator Equations
- Monotone Difference Schemes for Weakly Coupled Elliptic and Parabolic Systems
- An Introduction to the Analysis and Implementation of Sparse Grid Finite Element Methods
- Factorized Schemes of Second-Order Accuracy for Numerically Solving Unsteady Problems
- A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems
Artikel in diesem Heft
- Frontmatter
- On the Efficiency of a Family of Steffensen-Like Methods with Frozen Divided Differences
- Preconditioning Techniques Based on the Birkhoff–von Neumann Decomposition
- A Priori and A Posteriori Estimates of Conforming and Mixed FEM for a Kirchhoff Equation of Elliptic Type
- A Time-Stepping DPG Scheme for the Heat Equation
- Hybrid Spectral Difference Methods for an Elliptic Equation
- Simplified Iterated Lavrentiev Regularization for Nonlinear Ill-Posed Monotone Operator Equations
- Monotone Difference Schemes for Weakly Coupled Elliptic and Parabolic Systems
- An Introduction to the Analysis and Implementation of Sparse Grid Finite Element Methods
- Factorized Schemes of Second-Order Accuracy for Numerically Solving Unsteady Problems
- A Parameter Robust Finite Element Method for Fourth Order Singularly Perturbed Problems
