Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
ACM Transactions on Mathematical Software (TOMS)
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
A 3D Rectangular Mixed Finite Element Method to Solve the Stationary Semiconductor Equations
SIAM Journal on Scientific Computing
Splitting Techniques for the Unsteady Stokes Equations
SIAM Journal on Numerical Analysis
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Practical methods for optimal control using nonlinear programming
Practical methods for optimal control using nonlinear programming
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
A Note on Preconditioning Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Preconditioners for saddle point problems arising in computational fluid dynamics
Applied Numerical Mathematics
Block triangular preconditioners for symmetric saddle-point problems
Applied Numerical Mathematics - Numerical algorithms, parallelism and applications
A Preconditioner for Generalized Saddle Point Problems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
On Inexact Preconditioners for Nonsymmetric Matrices
SIAM Journal on Scientific Computing
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
Optimization of the parameterized Uzawa preconditioners for saddle point matrices
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
On HSS-based constraint preconditioners for generalized saddle-point problems
Numerical Algorithms
Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
Recently, Chen and Jiang [F. Chen, Y.-L. Jiang, A generalization of the inexact parameterized Uzawa methods for saddle point problems, Appl. Math. Comput. 206 (2008) 765-771] presented a parameterized inexact Uzawa (PIU) algorithm for solving symmetric saddle point problems, where the (1, 2)- and the (2, 1)-blocks are the transpose of each other. In this paper, we extend the PIU method to the block two-by-two linear system by allowing the (1, 2)-block to be not equal to the transpose of the (2, 1)-block and the (2, 2)-block may not be zero. We prove that the iteration method is convergent under certain conditions. With different choices of the parameter matrices, we obtain several new algorithms for solving the block two-by-two linear system. Numerical experiments confirm our theoretical results and show that our method is feasible and effective.