GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
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
Estimating the Attainable Accuracy of Recursively Computed Residual Methods
SIAM Journal on Matrix Analysis and Applications
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
Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning
SIAM Journal on Matrix Analysis and Applications
Theory of Inexact Krylov Subspace Methods and Applications to Scientific Computing
SIAM Journal on Scientific Computing
Inexact Krylov Subspace Methods for Linear Systems
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
Nonsymmetric saddle point problems arise in a wide variety of applications in computational science and engineering. The aim of this paper is to discuss the numerical behavior of several nonsymmetric iterative methods applied for solving the saddle point systems via the Schur complement reduction or the null-space projection approach. Krylov subspace methods often produce the iterates which fluctuate rather strongly. Here we address the question whether large intermediate approximate solutions reduce the final accuracy of these two-level (inner-outer) iteration algorithms. We extend our previous analysis obtained for symmetric saddle point problems and distinguish between three mathematically equivalent back-substitution schemes which lead to a different numerical behavior when applied in finite precision arithmetic. Theoretical results are then illustrated on a simple model example.