GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
SIAM Journal on Matrix Analysis and Applications
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
SIAM Journal on Scientific Computing
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
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
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
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)
Comparative Assessment of Algorithms and Software for Global Optimization
Journal of Global Optimization
On Using Reinforcement Learning to Solve Sparse Linear Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
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We evaluate performance profiles as a method for comparing preconditioners for iterative solvers by using them to address three questions that have previously been asked about incomplete LU preconditioners. For example, we use performance profiles to quantify the observation that if a system can be solved by a preconditioned iterative solver, then that solver is likely to use less space, and not much more time, than a direct solver. In contrast, we also observe that performance profiles are difficult to use for choosing specific parameter values. We end by discussing the role performance profiles might eventually play in helping users choose a preconditioner.