GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Topics in matrix analysis
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Computer Methods in Applied Mechanics and Engineering
Splitting techniques for the pseudospectral approximation of the unsteady Stokes equations
SIAM Journal on Numerical Analysis
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
SIAM Journal on Scientific Computing
A Note on Preconditioning for Indefinite Linear Systems
SIAM Journal on Scientific Computing
A Note on Preconditioning Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Block LU Preconditioners for Symmetric and Nonsymmetric Saddle Point Problems
SIAM Journal on Scientific Computing
Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
SIAM Journal on Scientific Computing
Inexact Matrix-Vector Products in Krylov Methods for Solving Linear Systems: A Relaxation Strategy
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
Block Preconditioners Based on Approximate Commutators
SIAM Journal on Scientific Computing
Preconditioners for Generalized Saddle-Point Problems
SIAM Journal on Numerical Analysis
Constraint Schur complement preconditioners for nonsymmetric saddle point problems
Applied Numerical Mathematics
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks
Journal of Computational and Applied Mathematics
Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
A preconditioned GLHSS iteration method for non-Hermitian singular saddle point problems
Computers & Mathematics with Applications
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We study block triangular Schur complement preconditioners for two by two block linear systems. Two block triangular Schur complement preconditioners are derived from a splitting of the (1,1)-block of the two by two block matrix. The two block triangular Schur complement preconditioners are different only in taking the opposite sign in the (2,2)-block (i.e. the Schur complement) of the preconditioners. We analyze the properties of the corresponding preconditioned matrices, in particular their spectra and discuss the computational performances of the preconditioned iterative methods. We show that fast convergence depends mainly on the quality of the splitting of the (1,1)-block. Moreover, we discuss some strategies of implementation of our preconditioners based on purely algebraic considerations. Thus, for applying our preconditioners to the Oseen equations we obtain preconditioning iterative methods in ''black box'' fashion.