Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
A parallel block multi-level preconditioner for the 3D incompressible Navier--Stokes equations
Journal of Computational Physics
Block triangular preconditioners for symmetric saddle-point problems
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
Block Preconditioners for LDG Discretizations of Linear Incompressible Flow Problems
Journal of Scientific Computing
Block preconditioners for LDG discretizations of linear incompressible flow problems
Journal of Scientific Computing
Computational Optimization and Applications
Positive stable block triangular preconditioners for symmetric saddle point problems
Applied Numerical Mathematics
Journal of Computational Physics
Iterative solvers and stabilisation for mixed electrostatic and magnetostatic formulations
Journal of Computational and Applied Mathematics
Constraint Schur complement preconditioners for nonsymmetric saddle point problems
Applied Numerical Mathematics
Some preconditioning techniques for linear systems
WSEAS Transactions on Mathematics
Comparing Some Methods and Preconditioners for Hydropower Plant Flow Simulations
High Performance Computing for Computational Science - VECPAR 2008
Optimization of the parameterized Uzawa preconditioners for saddle point matrices
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Applied Numerical Mathematics
The spectral properties of the preconditioned matrix for nonsymmetric saddle point problems
Journal of Computational and Applied Mathematics
Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D
Journal of Scientific Computing
Adaptive Time-Stepping for Incompressible Flow Part II: Navier-Stokes Equations
SIAM Journal on Scientific Computing
Preconditioning Saddle-Point Systems with Applications in Optimization
SIAM Journal on Scientific Computing
Optimal Solvers for PDE-Constrained Optimization
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
A Relaxed Dimensional Factorization preconditioner for the incompressible Navier-Stokes equations
Journal of Computational Physics
Stabilization and scalable block preconditioning for the Navier-Stokes equations
Journal of Computational Physics
Preconditioning Stochastic Galerkin 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
Preconditioning Iterative Methods for the Optimal Control of the Stokes Equations
SIAM Journal on Scientific Computing
A note on spectrum analysis of augmentation block Schur complement preconditioners
Numerical Algorithms
Substructure preconditioners for a class of structured linear systems of equations
Mathematical and Computer Modelling: An International Journal
Preconditioning for Allen-Cahn variational inequalities with non-local constraints
Journal of Computational Physics
A preconditioning technique for Schur complement systems arising in stochastic optimization
Computational Optimization and Applications
SIAM Journal on Scientific Computing
A robust finite element solver for a multiharmonic parabolic optimal control problem
Computers & Mathematics with Applications
Indefinite block triangular preconditioner for symmetric saddle point problems
Calcolo: a quarterly on numerical analysis and theory of computation
Preconditioning for large scale micro finite element analyses of 3d poroelasticity
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
Journal of Scientific Computing
Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Prescribing the behavior of early terminating GMRES and Arnoldi iterations
Numerical Algorithms
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Preconditioners are often conceived as approximate inverses. For nonsingular indefinite matrices of saddle-point (or KKT) form, we show how preconditioners incorporating an exact Schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues. Thus approximations of the Schur complement lead to preconditioners which can be very effective even though they are in no sense approximate inverses.