GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Machine Learning
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
Preconditioning sparse matrices for computing eigenvalues and solving linear systems of equations
Preconditioning sparse matrices for computing eigenvalues and solving linear systems of equations
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)
On Using Reinforcement Learning to Solve Sparse Linear Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
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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We evaluate the effectiveness of neural networks as a tool for predicting whether a particular combination of preconditioner and iterative method will correctly solve a given sparse linear system Ax= b. We consider several scenarios corresponding to different assumptions about the relationship between the systems used to train the neural network and those for which the neural network is expected to predict behavior. Greater similarity between those two sets leads to better accuracy, but even when the two sets are very different prediction accuracy can be improved by using additional computation.