Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives
DOI10.5402/2012/127647zbMath1264.65037OpenAlexW1969138095WikidataQ58689797 ScholiaQ58689797MaRDI QIDQ1954336
Publication date: 11 June 2013
Published in: ISRN Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.5402/2012/127647
History of mathematics in the 21st century (01A61) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Iterative numerical methods for linear systems (65F10) History of numerical analysis (65-03) Preconditioners for iterative methods (65F08)
Related Items (14)
Uses Software
Cites Work
- Decay Rates for Inverses of Band Matrices
- Modification of the minimum-degree algorithm by multiple elimination
- GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
- Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method
- Preconditioned conjugate gradients for solving the transient Boussinesq equations in three-dimensional geometries
- CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
- The Evolution of the Minimum Degree Ordering Algorithm
- An Algorithm for Scaling Matrices
- Fast solution to finite element flow equations by newton iteration and modified conjugate gradient method
- Generalized Nested Dissection
- Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients
- Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
- Mixed and Hybrid Finite Element Methods
- Ordering Methods for Preconditioned Conjugate Gradient Methods Applied to Unstructured Grid Problems
- Approximate inverse preconditionings for sparse linear systems
- Factorized Sparse Approximate Inverse Preconditionings I. Theory
- Solution of Sparse Indefinite Systems of Linear Equations
- An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
- Multi-Level Adaptive Solutions to Boundary-Value Problems
- A class of first order factorization methods
- Orderings for Incomplete Factorization Preconditioning of Nonsymmetric Problems
- Fast Iterative Solution of Stabilised Stokes Systems Part II: Using General Block Preconditioners
- Preconditioned conjugate gradient methods for three‐dimensional linear elasticity
- A Linear Algebraic Analysis of Diffusion Synthetic Acceleration for the Boltzmann Transport Equation
- Numerical performance of projection methods in finite element consolidation models
- PARTITIONED SOLUTION PROCEDURE FOR SIMULTANEOUS INTEGRATION OF COUPLED-FIELD PROBLEMS
- Preconditioning Chebyshev Spectral Collocation by Finite-Difference Operators
- Parallel Preconditioning with Sparse Approximate Inverses
- ILUS: An incomplete LU preconditioner in sparse skyline format
- An improved incomplete Cholesky factorization
- A Field-Based Mixed Formulation for the Two-Dimensional Magnetostatic Problem
- Sparse Approximate-Inverse Preconditioners Using Norm-Minimization Techniques
- A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
- Approximate Inverse Preconditioners via Sparse-Sparse Iterations
- Fast iterative solution of large undrained soil-structure interaction problems
- A Robust and Efficient ILU that Incorporates the Growth of the Inverse Triangular Factors
- Crout Versions of ILU for General Sparse Matrices
- Scaling improves stability of preconditioned CG-like solvers for FE consolidation equations
- A Multigrid Tutorial, Second Edition
- Sparse Approximate Inverse Smoother for Multigrid
- Constraint Preconditioning for Indefinite Linear Systems
- A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
- A Note on Preconditioning for Indefinite Linear Systems
- Problem-dependent preconditioners for iterative solvers in FE elastostatics
- Sparse Approximate Inverses and Target Matrices
- On Generalizing the Algebraic Multigrid Framework
- A Parallel Graph Coloring Heuristic
- The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier‐Stokes equations
- BILUTM: A Domain-Based Multilevel Block ILUT Preconditioner for General Sparse Matrices
- BILUM: Block Versions of Multielimination and Multilevel ILU Preconditioner for General Sparse Linear Systems
- Incomplete Cholesky Factorizations with Limited Memory
- Numerical comparison of preconditionings for large sparse finite element problems
- Parallel Algebraic Multigrid Methods on Distributed Memory Computers
- An efficient diagonal preconditioner for finite element solution of Biot's consolidation equations
- Direct, partitioned and projected solution to finite element consolidation models
- Block-diagonal and indefinite symmetric preconditioners for mixed finite element formulations
- Preconditioning Legendre Spectral Collocation Approximations to Elliptic Problems
- Diagonally compensated reduction and related preconditioning methods
- New convergence results and preconditioning strategies for the conjugate gradient method
- GMRESR: a family of nested GMRES methods
- ILUT: A dual threshold incomplete LU factorization
- Any Nonincreasing Convergence Curve is Possible for GMRES
- A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
- On eigenvalue distribution of constraint‐preconditioned symmetric saddle point matrices
- Efficient parallel solution to large‐size sparse eigenproblems with block FSAI preconditioning
- Linear Algebra Methods in a Mixed Approximation of Magnetostatic Problems
- A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
- Constraint-Style Preconditioners for Regularized Saddle Point Problems
- ARMS: an algebraic recursive multilevel solver for general sparse linear systems
- A robust incomplete factorization preconditioner for positive definite matrices
- Indefinitely preconditioned conjugate gradient method for large sparse equality and inequality constrained quadratic problems
- A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods
- Adaptive Algebraic Multigrid
- Parallel Algebraic Multigrids for Structural Mechanics
- Multilevel Preconditioners Constructed From Inverse-Based ILUs
- Toward an h-Independent Algebraic Multigrid Method for Maxwell's Equations
- Aggregation-Based Algebraic Multilevel Preconditioning
- Reducing Complexity in Parallel Algebraic Multigrid Preconditioners
- The Use of Pre-conditioning in Iterative Methods for Solving Linear Equations with Symmetric Positive Definite Matrices
- On the Automatic Scaling of Matrices for Gaussian Elimination
- Nested Dissection of a Regular Finite Element Mesh
- Methods of conjugate gradients for solving linear systems
- Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow
- Finite element preconditioning on spectral element discretizations for coupled elliptic equations
- Applications of symmetric and nonsymmetric MSSOR preconditioners to large-scale Biot's consolidation problems with nonassociated plasticity
- A modified SSOR preconditioning strategy for Helmholtz equations
- Parallel Rayleigh quotient optimization with FSAI-based preconditioning
- FSAI-based parallel mixed constraint preconditioners for saddle point problems arising in geomechanics
- A numerical study on preconditioning and partitioning schemes for reactive transport in a PEMFC catalyst layer
- RMCP: relaxed mixed constraint preconditioners for saddle point linear systems arising in geomechanics
- Numerical simulation of fluid-structure interaction problems on hybrid meshes with algebraic multigrid methods
- Algebraic multigrid preconditioners for the bidomain reaction-diffusion system
- A new preconditioning technique for solving large sparse linear systems
- Piecewise bilinear preconditioning of high-order finite element method
- A wavelet-based algebraic multigrid preconditioner for sparse linear systems
- Factored sparse approximate inverse of block tridiagonal and block pentadiagonal matrices
- A parallel multigrid-based preconditioner for the 3D heterogeneous high-frequency Helmholtz equation
- Mixed constraint preconditioners for the iterative solution of FE coupled consolidation equations
- A comparison of projective and direct solvers for finite elements in elastostatics
- Novel preconditioners for the iterative solution to FE-discretized coupled consolidation equations
- A survey of preconditioned iterative methods for linear systems of algebraic equations
- Parallel implementation of multifrontal schemes
- Algebraic multilevel preconditioning methods. I
- Approximating the inverse of a matrix for use in iterative algorithms on vector processors
- QMR: A quasi-minimal residual method for non-Hermitian linear systems
- A class of iterative methods for finite element equations
- The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations
- The effect of ordering on preconditioned conjugate gradients
- Approximate sparsity patterns for the inverse of a matrix and preconditioning
- A comparative study of sparse approximate inverse preconditioners
- Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations
- Sparse approximate inverse smoothers for geometric and algebraic multigrid
- A parallel solver for large-scale Markov chains
- \textit{BoomerAMG}: A parallel algebraic multigrid solver and preconditioner
- Experimental study of ILU preconditioners for indefinite matrices
- Computational experience with sequential and parallel, preconditioned Jacobi--Davidson for large, sparse symmetric matrices
- Parallel multigrid smoothing: Polynomial versus Gauss--Seidel
- Factorized sparse approximate inverses for preconditioning
- Modeling and simulation of a class of coupled thermo-chemo-mechanical processes in multiphase solids.
- Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
- Iterative solution of linear systems in the 20th century
- Algebraic multigrid for higher-order finite elements
- Factorized-sparse-approximate-inverse preconditionings of linear systems with unsymmetric matrices
- Multilevel ILU decomposition
- Algebraic multigrid theory: The symmetric case
- Block triangular preconditioners for symmetric saddle-point problems
- Preconditioning techniques for large linear systems: A survey
- Preconditioning indefinite systems in interior point methods for optimization
- Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
- Nested Krylov methods based on GCR
- A generalized block FSAI preconditioner for nonsymmetric linear systems
- A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations
- On the eigenvalues of a class of saddle point matrices
- Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems
- Mixed constraint preconditioning in computational contact mechanics
- Efficient algebraic multigrid for migration-diffusion-convection-reaction systems arising in electrochemical simulations
- Inexact constraint preconditioners for linear systems arising in interior point methods
- Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
- A Scalable Parallel Algorithm for Incomplete Factor Preconditioning
- Approximate inverse preconditioning in the parallel solution of sparse eigenproblems
- Factorized sparse approximate inverse preconditionings. IV: Simple approaches to rising efficiency
- Multiresolution Approximate Inverse Preconditioners
- A Factored Approximate Inverse Preconditioner with Pivoting
- The role of preconditioning in the solution to FE coupled consolidation equations by Krylov subspace methods
- Preconditioners in computational geomechanics: A survey
- Enhanced Block FSAI Preconditioning Using Domain Decomposition Techniques
- Shifted FSAI preconditioners for the efficient parallel solution of non-linear groundwater flow models
- Thermo-hydro-mechanical modeling of fluid geological storage by Godunov-mixed methods
- A Block FSAI-ILU Parallel Preconditioner for Symmetric Positive Definite Linear Systems
- A power sparse approximate inverse preconditioning procedure for large sparse linear systems
- Truly monolithic algebraic multigrid for fluid-structure interaction
- Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
- A new perspective on strength measures in algebraic multigrid
- Multigrid Smoothers for Ultraparallel Computing
- Adaptive Pattern Research for Block FSAI Preconditioning
- Algebraic Multilevel Preconditioning Methods, II
- A robust incomplete Choleski-conjugate gradient algorithm
- Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
- Recent computational developments in Krylov subspace methods for linear systems
- Algebraic multigrid (AMG) for saddle point systems from meshfree discretizations
- Algebraic multilevel preconditioning of finite element matrices using local Schur complements
- Numerical solution of saddle point problems
- Direct Methods for Sparse Linear Systems
- A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations
- Multilevel Block Factorization Preconditioners
- An overview of the Trilinos project
- An Algebraic Multigrid Preconditioner for a Class of Singular M-Matrices
- Interpolation Operators for Algebraic Multigrid by Local Optimization
- Performance and robustness of block constraint preconditioners in finite element coupled consolidation problems
- Algebraic multigrid and algebraic multilevel methods: a theoretical comparison
- Eigenvalue estimates for preconditioned saddle point matrices
- Algebraic Multigrid Solvers for Complex-Valued Matrices
- Multi-level incomplete factorizations for the iterative solution of non-linear finite element problems
- The Multifrontal Solution of Indefinite Sparse Symmetric Linear
- Polynomial Preconditioners for Conjugate Gradient Calculations
- A review of algebraic multigrid
- Geometric multigrid with applications to computational fluid dynamics
- A fully coupled dynamic model for two-phase fluid flow in deformable porous media
- Parallel incomplete factorizations with pseudo-overlapped subdomains
- Parallel algebraic multigrid based on subdomain blocking
- A robust ILU with pivoting based on monitoring the growth of the inverse factors
- A multilevel AINV preconditioner
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Preconditioning for sparse linear systems at the dawn of the 21st century: history, current developments, and future perspectives