A compact row storage scheme for Cholesky factors using elimination trees
ACM Transactions on Mathematical Software (TOMS)
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
An extended set of FORTRAN basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The influence of relaxed supernode partitions on the multifrontal method
ACM Transactions on Mathematical Software (TOMS)
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
Compressed graphs and the minimum degree algorithm
SIAM Journal on Scientific Computing
QMRPACK: a package of QMR algorithms
ACM Transactions on Mathematical Software (TOMS)
Performance issues for iterative solvers in device simulation
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Matrix computations (3rd ed.)
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
Approximate Inverse Techniques for Block-Partitioned Matrices
SIAM Journal on Scientific Computing
An object-oriented framework for block preconditioning
ACM Transactions on Mathematical Software (TOMS)
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
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
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
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
A Robust and Efficient ILU that Incorporates the Growth of the Inverse Triangular Factors
SIAM Journal on Scientific Computing
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
Multilevel Preconditioners Constructed From Inverse-Based ILUs
SIAM Journal on Scientific Computing
A Recommendation System for Preconditioned Iterative Solvers
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
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Three techniques for improving the robustness and performance of incomplete factorization preconditioners for sparse systems with symmetric positive definite or mildly indefinite coefficient matrices are introduced. The primary contribution is two new block algorithms for incomplete factorization that result in an improvement in the performance of both the preconditioner generation and the iterative solution phases. One of the algorithms applies to matrices that have a natural block structure in their original form, and the other applies to matrices without natural dense blocks. Additionally, two relatively simple but highly effective heuristic strategies are introduced. These include selecting the solver based on the definiteness properties of the preconditioner and automatic selection and tuning of incomplete factorization parameters. All three techniques have adaptive components; i.e., the preconditioner-solver combination chooses parameters or algorithmic components based on the properties of the coefficient matrix and its incomplete factors. Two of the three techniques are applicable to incomplete LU factorization for unsymmetric systems as well.