GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
SIAM Journal on Scientific Computing
On Inexact Preconditioners for Nonsymmetric Matrices
SIAM Journal on Scientific Computing
An Algebraic Analysis of a Block Diagonal Preconditioner for Saddle Point Systems
SIAM Journal on Matrix Analysis and Applications
Approximate Factorization Constraint Preconditioners for Saddle-Point Matrices
SIAM Journal on Scientific Computing
A Class of Nonsymmetric Preconditioners for Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
Preconditioners for Generalized Saddle-Point Problems
SIAM Journal on Numerical Analysis
Algorithm 866: IFISS, a Matlab toolbox for modelling incompressible flow
ACM Transactions on Mathematical Software (TOMS)
Constraint-Style Preconditioners for Regularized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
Constraint Schur complement preconditioners for nonsymmetric saddle point problems
Applied Numerical Mathematics
Combination Preconditioning and the Bramble-Pasciak$^{+}$ Preconditioner
SIAM Journal on Matrix Analysis and Applications
Optimization of the parameterized Uzawa preconditioners for saddle point matrices
Journal of Computational and Applied Mathematics
Constraint Preconditioners for Symmetric Indefinite Matrices
SIAM Journal on Matrix Analysis and Applications
Hi-index | 7.29 |
Based on matrix splittings, a new alternating preconditioner with two parameters is proposed for solving saddle point problems. Some theoretical analyses for the eigenvalues of the associated preconditioned matrix are given. The choice of the parameters is considered and the quasi-optimal parameters are obtained. The new preconditioner with these quasi-optimal parameters significantly improves the convergence rate of the generalized minimal residual (GMRES) iteration. Numerical experiments from the linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially on the larger viscosity parameter @n. Further extensions of the preconditioner to generalized saddle point matrices are also checked.