Inexact and preconditioned Uzawa algorithms for saddle point problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
An Efficient Iterative Method for the Generalized Stokes Problem
SIAM Journal on Scientific Computing
Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
SIAM Journal on Scientific Computing
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
An Iterative Method with Variable Relaxation Parameters for Saddle-Point Problems
SIAM Journal on Matrix Analysis and Applications
Analysis of iterative methods for saddle point problems: a unified approach
Mathematics of Computation
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
On the convergence of iterative methods for solving singular linear systems
Journal of Computational and Applied Mathematics
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
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Constraint Preconditioners for Symmetric Indefinite Matrices
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Matrix Analysis and Applications
Convergence of General Nonstationary Iterative Methods for Solving Singular Linear Equations
SIAM Journal on Matrix Analysis and Applications
The generalized HSS method for solving singular linear systems
Journal of Computational and Applied Mathematics
Constraint preconditioners for solving singular 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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Recently, Zheng, Bai and Yang studied the parameterized Uzawa method for solving singular saddle point problems (B. Zheng, Z.-Z. Bai, X. Yang, On semi-convergence of parameterized Uzawa methods for singular saddle point problems, Linear Algebra Appl. 431 (2009) 808-817). In this paper, we discuss the inexact Uzawa method, which covers the Uzawa method, the preconditioned Uzawa method, and the parameterized Uzawa method to solve the singular saddle point problems. We prove the semi-convergence result under restrictions by verifying two necessary and sufficient conditions, that is, all elementary divisors associated with the eigenvalue 1 of its iterative matrix are linear, and the pseudo-spectral radius of the iterative matrix is less than 1. Sufficient conditions for the semi-convergence of several Uzawa-type methods are also provided. In addition, numerical examples are given to demonstrate the semi-convergence of Uzawa-type methods.