A Restarted GMRES Method Augmented with Eigenvectors
SIAM Journal on Matrix Analysis and Applications
A Deflation Technique for Linear Systems of Equations
SIAM Journal on Scientific Computing
Adaptively Preconditioned GMRES Algorithms
SIAM Journal on Scientific Computing
Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
SIAM Journal on Matrix Analysis and Applications
GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
Truncation Strategies for Optimal Krylov Subspace Methods
SIAM Journal on Numerical Analysis
A Class of Spectral Two-Level Preconditioners
SIAM Journal on Scientific Computing
Numerical Approximation of Partial Differential Equations
Numerical Approximation of Partial Differential Equations
Preconditioner updates applied to CFD model problems
Applied Numerical Mathematics
Improving Triangular Preconditioner Updates for Nonsymmetric Linear Systems
Large-Scale Scientific Computing
Preconditioning Newton---Krylov methods in nonconvex large scale optimization
Computational Optimization and Applications
| Hi-index | 7.29 |
The use of preconditioned Krylov methods is in many applications mandatory for computing efficiently the solution of large sparse nonlinear systems of equations. However, the available preconditioners are often sub-optimal, due to the changing nature of the linearized operator. In this work we introduce and analyse an adaptive preconditioning technique based on the Krylov subspace information generated at previous steps in the nonlinear iteration. In particular, we use an adaptive technique suggested in [J. Baglama, D. Calvetti, G.H. Golub, L. Reichel, Adaptively preconditioned GMRES algorithms, SIAM J. Sci. Comput. 20(1) (1998) 243-269] for restarted GMRES to enhance existing preconditioners with information available from previous stages in the nonlinear iteration. Numerical experiments drawn from domain decomposition techniques and fluid flow applications are used to validate the increased efficiency of our approach.