GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Mining and visualizing recommendation spaces for elliptic PDEs with continuous attributes
ACM Transactions on Mathematical Software (TOMS) - Special issue in honor of John Rice's 65th birthday
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
Sparse Distributed Memory
Introduction to Reinforcement Learning
Introduction to Reinforcement Learning
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
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
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 836: COLAMD, a column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Neural Networks for Predicting the Behavior of Preconditioned Iterative Solvers
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Using performance profiles to evaluate preconditioners for iterative methods
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
Towards Low-Cost, High-Accuracy Classifiers for Linear Solver Selection
ICCS '09 Proceedings of the 9th International Conference on Computational Science: Part I
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This paper describes how reinforcement learning can be used to select from a wide variety of preconditioned solvers for sparse linear systems. This approach provides a simple way to consider complex metrics of goodness, and makes it easy to evaluate a wide range of preconditioned solvers. A basic implementation recommends solvers that, when they converge, generally do so with no more than a 17% overhead in time over the best solver possible within the test framework. Potential refinements of, and extensions to, the system are discussed.