The convergence factor of preconditioned algorithms of the Arrow-Hurwicz type
SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
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
Fast iterative solution of stabilised Stokes systems part II: using general block preconditioners
SIAM Journal on Numerical Analysis
Analysis of the Inexact Uzawa Algorithm for Saddle Point Problems
SIAM Journal on Numerical Analysis
On the convergence of iterative methods for stabilized saddle point problems
International Journal of Computer Mathematics
A robust PDE solver for the 3D Stokes/Navier-Stokes systems on the grid environment
GRID '07 Proceedings of the 8th IEEE/ACM International Conference on Grid Computing
Analysis of the nonlinear Uzawa algorithm for symmetric saddle point problems
International Journal of Computer Mathematics
Spectral properties of primal-based penalty preconditioners for saddle point problems
Journal of Computational and Applied Mathematics
SIAM Journal on Matrix Analysis and Applications
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
Eigenvalue Estimates for Preconditioned Nonsymmetric Saddle Point Matrices
SIAM Journal on Matrix Analysis and Applications
Preconditioning Iterative Methods for the Optimal Control of the Stokes Equations
SIAM Journal on Scientific Computing
A statistical multiresolution strategy for image reconstruction
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Indefinite block triangular preconditioner for symmetric saddle point problems
Calcolo: a quarterly on numerical analysis and theory of computation
Journal of Scientific Computing
Semi-convergence analysis of Uzawa methods for singular saddle point problems
Journal of Computational and Applied Mathematics
Eigenvalue estimates of an indefinite block triangular preconditioner for saddle point problems
Journal of Computational and Applied Mathematics
Hierarchical Krylov and nested Krylov methods for extreme-scale computing
Parallel Computing
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In this paper two classes of iterative methods for saddle point problems are considered: inexact Uzawa algorithms and a class of methods with symmetric preconditioners. In both cases the iteration matrix can be transformed to a symmetric matrix by block diagonal matrices, a simple but essential observation which allows one to estimate the convergence rate of both classes by studying associated eigenvalue problems. The obtained estimates apply for a wider range of situations and are partially sharper than the known estimates in literature. A few numerical tests are given which confirm the sharpness of the estimates.