GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Direct methods for sparse matrices
Direct methods for sparse matrices
A stability analysis of incomplete LU factorizations
Mathematics of Computation
Multicolor ICCG methods for vector computers
SIAM Journal on Numerical Analysis
Sparsity structure and Gaussian elimination
ACM SIGNUM Newsletter
Preconditioning techniques for nonsymmetric and indefinite linear systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
On the robustness of Ilu smoothing
SIAM Journal on Scientific and Statistical Computing
Krylov subspace methods on supercomputers
SIAM Journal on Scientific and Statistical Computing
A block ordering method for sparse matrices
SIAM Journal on Scientific and Statistical Computing
A history of scientific computing
A history of scientific computing
A new modified Cholesky factorization
SIAM Journal on Scientific and Statistical Computing
Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
Limits on parallelism in the numerical solution of linear partial differential equations
SIAM Journal on Scientific and Statistical Computing
The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors
Proceedings of a conference on Preconditioned conjugate gradient methods
On parallelism and convergence of incomplete LU factorizations
Applied Numerical Mathematics - Selected papers CWI-IMACS Symposia on Parallel Scientific Computing, Amsterdam, Netherlands
Predicting the behavior of finite precision Lanczos and conjugate gradient computations
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific and Statistical Computing
A review on the inverse of symmetric tridiagonal and block tridiagonal matrices
SIAM Journal on Matrix Analysis and Applications
Ordering methods for preconditioned conjugate gradient methods applied to unstructured grid problems
SIAM Journal on Matrix Analysis and Applications
Parallel ocean general circulation modeling
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Scalable iterative solution of sparse linear systems
Parallel Computing
Predicting Structure in Sparse Matrix Computations
SIAM Journal on Matrix Analysis and Applications
An improved incomplete Cholesky factorization
ACM Transactions on Mathematical Software (TOMS)
Algorithm 740: Fortran subroutines to compute improved incomplete Cholesky factorizations
ACM Transactions on Mathematical Software (TOMS)
Iterative solution methods
A linear algebraic analysis of diffusion synthetic acceleration for the Boltzmann transport equation
SIAM Journal on Numerical Analysis
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Compressed graphs and the minimum degree algorithm
SIAM Journal on Scientific Computing
Nested grids ILU-decomposition (NGILU)
Proceedings of the 6th international congress on Computational and applied mathematics
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
Any Nonincreasing Convergence Curve is Possible for GMRES
SIAM Journal on Matrix Analysis and Applications
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
An Approximate Minimum Degree Ordering Algorithm
SIAM Journal on Matrix Analysis and Applications
Matrix computations (3rd ed.)
Projection methods for linear systems
Journal of Computational and Applied Mathematics - Special issue: ROLLS symposium
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Iterative methods for solving linear systems
Iterative methods for solving linear systems
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)
Sparse Approximate-Inverse Preconditioners Using Norm-Minimization Techniques
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
On a Class of Preconditioning Methods for Dense Linear Systems from Boundary Elements
SIAM Journal on Scientific Computing
Parallelism in ILU-preconditioned GMRES
Parallel Computing
The Incomplete Factorization Multigraph Algorithm
SIAM Journal on Scientific Computing
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
A comparative study of sparse approximate inverse preconditioners
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
SIAM Journal on Scientific Computing
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
Matrix Renumbering ILU: An Effective Algebraic Multilevel ILU Preconditioner for Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Incomplete Cholesky Factorizations with Limited Memory
SIAM Journal on Scientific Computing
BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
A multilevel block incomplete factorization preconditioning
Applied Numerical Mathematics
Ordering, Anisotropy, and Factored Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Wavelet Methods for Second-Order Elliptic Problems, Preconditioning, and Adaptivity
SIAM Journal on Scientific Computing
Parallel Computing - Special Anniversary issue
Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration
SIAM Journal on Scientific Computing
The fast multipole method: numerical implementation
Journal of Computational Physics
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Orderings for Factorized Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Robustness and Scalability of Algebraic Multigrid
SIAM Journal on Scientific Computing
Sparse Approximate Inverse Smoother for Multigrid
SIAM Journal on Matrix Analysis and Applications
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
Optimal Order Preconditioning of Finite Difference Matrices
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
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
Preconditioning eigenvalues and some comparison of solvers
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Refining an approximate inverse
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
A review of algebraic multigrid
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Multigrid
Parallel preconditioning of a sparse eigensolver
Parallel Computing - Linear systems and associated problems
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
FQMR: A Flexible Quasi-Minimal Residual Method with Inexact Preconditioning
SIAM Journal on Scientific Computing
Multiresolution Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Robust Parallel Smoothing for Multigrid Via Sparse Approximate Inverses
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
A Structural Diagnosis of Some IC Orderings
SIAM Journal on Scientific Computing
An Algebraic Multilevel Multigraph Algorithm
SIAM Journal on Scientific Computing
A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
SIAM Journal on Scientific Computing
Algebraic Multilevel Methods and Sparse Approximate Inverses
SIAM Journal on Matrix Analysis and Applications
On the Relations between ILUs and Factored Approximate Inverses
SIAM Journal on Matrix Analysis and Applications
An Analysis of Sparse Approximate Inverse Preconditioners for Boundary Integral Equations
SIAM Journal on Matrix Analysis and Applications
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
A Factored Approximate Inverse Preconditioner with Pivoting
SIAM Journal on Matrix Analysis and Applications
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
A Multilevel Dual Reordering Strategy for Robust Incomplete LU Factorization of Indefinite Matrices
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Incomplete Multilevel Cholesky Factorizations
SIAM Journal on Matrix Analysis and Applications
The Fast Multipole Method I: Error Analysis and Asymptotic Complexity
SIAM Journal on Numerical Analysis
Sparse approximate inverse smoothers for geometric and algebraic multigrid
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
A parallel solver for large-scale Markov chains
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
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
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Application of Threshold Partitioning of Sparse Matrices to Markov Chains
IPDS '96 Proceedings of the 2nd International Computer Performance and Dependability Symposium (IPDS '96)
Krylov methods for the numerical solution of initial-value problems in differential-algebraic equations
New sequential and scalable parallel algorithms for incomplete factor preconditioning
New sequential and scalable parallel algorithms for incomplete factor preconditioning
SIAM Journal on Scientific Computing
Exploiting Multilevel Preconditioning Techniques in Eigenvalue Computations
SIAM Journal on Scientific Computing
On a class of preconditioners for solving the Helmholtz equation
Applied Numerical Mathematics
An MPI Implementation of the SPAI Preconditioner on the T3E
International Journal of High Performance Computing Applications
International Journal of High Performance Computing Applications
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
A finite element algorithm for reanalysis of structures with added degrees of freedom
Finite Elements in Analysis and Design
An implicit compact scheme solver with application to chemically reacting flows
Journal of Computational Physics
Journal of Computational Physics
On the discrete dynamic nature of the conjugate gradient method
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Numerical performance of incomplete factorizations for 3D transient convection-diffusion problems
Advances in Engineering Software
Iteratively constructing preconditioners via the conjugate gradient method
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Object-oriented programming of distributed iterative equation solvers
Computers and Structures
Additive preconditioning and aggregation in matrix computations
Computers & Mathematics with Applications
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Preconditioners for the conjugate gradient algorithm using Gram-Schmidt and least squares methods
International Journal of Computer Mathematics
Acceleration of Preconditioned Krylov Solvers for Bubbly Flow Problems
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
On Using Reinforcement Learning to Solve Sparse Linear Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Schur aggregation for linear systems and determinants
Theoretical Computer Science
FGMRES preconditioning by symmetric/skew-symmetric decomposition of generalized stokes problems
Mathematics and Computers in Simulation
Some preconditioning techniques for linear systems
WSEAS Transactions on Mathematics
Optimization of the parameterized Uzawa preconditioners for saddle point matrices
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
On Single Precision Preconditioners for Krylov Subspace Iterative Methods
Large-Scale Scientific Computing
Advances in Engineering Software
Lanczos-type variants of the COCR method for complex nonsymmetric linear systems
Journal of Computational Physics
Efficient Parallelization of the Preconditioned Conjugate Gradient Method
PaCT '09 Proceedings of the 10th International Conference on Parallel Computing Technologies
Journal of Computational and Applied Mathematics
Journal of Computational Physics
New implementation of QMR-type algorithms
Computers and Structures
Journal of Computational and Applied Mathematics
Computational Optimization and Applications
A directed Monte Carlo solution of linear stochastic algebraic system of equations
Finite Elements in Analysis and Design
Acceleration of preconditioned Krylov solvers for bubbly flow problems
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part I
Additive preconditioning for matrix computations
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
A comparative study of iterative solutions to linear systems arising in quantum mechanics
Journal of Computational Physics
Algebraic and numerical algorithms
Algorithms and theory of computation handbook
On the performance of parallel normalized explicit preconditioned conjugate gradient type methods
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Journal of Computational Physics
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
Iterative Near-Field Preconditioner for the Multilevel Fast Multipole Algorithm
SIAM Journal on Scientific Computing
A Block FSAI-ILU Parallel Preconditioner for Symmetric Positive Definite Linear Systems
SIAM Journal on Scientific Computing
Fast iterative solvers for thin structures
Finite Elements in Analysis and Design
Preconditioning the bidomain model with almost linear complexity
Journal of Computational Physics
Acquired Clustering Properties and Solution of Certain Saddle Point Systems
SIAM Journal on Matrix Analysis and Applications
MINRES-QLP: A Krylov Subspace Method for Indefinite or Singular Symmetric Systems
SIAM Journal on Scientific Computing
Improved Scaling for Quantum Monte Carlo on Insulators
SIAM Journal on Scientific Computing
Performance analysis of block jacobi preconditioning technique based on block broyden method
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Advances in Engineering Software
Advancing matrix computations with randomized preprocessing
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
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
An approach for structural static reanalysis with unchanged number of degrees of freedom
Structural and Multidisciplinary Optimization
Journal of Computational Physics
Solution of generalized shifted linear systems with complex symmetric matrices
Journal of Computational Physics
An Empirical Analysis of the Performance of Preconditioners for SPD Systems
ACM Transactions on Mathematical Software (TOMS)
On iterative techniques for computing flow in large two-dimensional discrete fracture networks
Journal of Computational and Applied Mathematics
Minimizing Condition Number via Convex Programming
SIAM Journal on Matrix Analysis and Applications
Staggered meshless solid-fluid coupling
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Journal of Computational Physics
Solving Hermitian positive definite systems using indefinite incomplete factorizations
Journal of Computational and Applied Mathematics
Data Mining and Knowledge Discovery
Multigrid in energy preconditioner for Krylov solvers
Journal of Computational Physics
Journal of Computational Physics
Towards a recursive iterative preconditioner
Proceedings of the 51st ACM Southeast Conference
VBARMS: A variable block algebraic recursive multilevel solver for sparse linear systems
Journal of Computational and Applied Mathematics
A generalization of the optimal diagonal approximate inverse preconditioner
Computers & Mathematics with Applications
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.54 |
This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices. Covered topics include progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions. Some of the challenges ahead are also discussed. An extensive bibliography completes the paper.