Domain decomposition algorithms with small overlap
SIAM Journal on Scientific Computing
An improved incomplete Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
Fast and effective algorithms for graph partitioning and sparse-matrix ordering
IBM Journal of Research and Development - Special issue: optical lithography I
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
A parallel algorithm for multilevel graph partitioning and sparse matrix ordering
Journal of Parallel and Distributed Computing
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
A comparative study of sparse approximate inverse preconditioners
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
SIAM Journal on Scientific Computing
BoomerAMG: a parallel algebraic multigrid solver and preconditioner
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
International Journal of High Performance Computing Applications
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Balanced Incomplete Factorization
SIAM Journal on Scientific Computing
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
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Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choices of solvers, preconditioners, and their parameters. The diversity of preconditioners makes it difficult to analyze them in a unified theoretical model. A systematic empirical evaluation of existing preconditioned iterative solvers can help in identifying the relative advantages of various implementations. We present the results of a comprehensive experimental study of the most popular preconditioner and iterative solver combinations for symmetric positive-definite systems. We introduce a methodology for a rigorous comparative evaluation of various preconditioners, including the use of some simple but powerful metrics. The detailed comparison of various preconditioner implementations and a state-of-the-art direct solver gives interesting insights into their relative strengths and weaknesses. We believe that these results would be useful to researchers developing preconditioners and iterative solvers as well as practitioners looking for appropriate sparse solvers for their applications.