The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Deflation of conjugate gradients with applications to boundary value problems
SIAM Journal on Numerical Analysis
On the order of prolongations and restrictions in multigrid procedures
Journal of Computational and Applied Mathematics
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A Restarted GMRES Method Augmented with Eigenvectors
SIAM Journal on Matrix Analysis and Applications
Restarted GMRES preconditioned by deflation
Journal of Computational and Applied Mathematics
Coarse-Grid Correction for Nonelliptic and Singular Perturbation Problems
SIAM Journal on Scientific Computing
Adaptively Preconditioned GMRES Algorithms
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Deflated Version of the Conjugate Gradient Algorithm
SIAM Journal on Scientific Computing
Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
SIAM Journal on Matrix Analysis and Applications
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Analysis of acceleration strategies for restarted minimal residual methods
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
A Class of Spectral Two-Level Preconditioners
SIAM Journal on Scientific Computing
Recycling Subspace Information for Diffuse Optical Tomography
SIAM Journal on Scientific Computing
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Incremental spectral preconditioners for sequences of linear systems
Applied Numerical Mathematics
Additive and Multiplicative Two-Level Spectral Preconditioning for General Linear Systems
SIAM Journal on Scientific Computing
Multilevel Projection-Based Nested Krylov Iteration for Boundary Value Problems
SIAM Journal on Scientific Computing
Deflation and Balancing Preconditioners for Krylov Subspace Methods Applied to Nonsymmetric Matrices
SIAM Journal on Matrix Analysis and Applications
Journal of Scientific Computing
A Coarse Space Construction Based on Local Dirichlet-to-Neumann Maps
SIAM Journal on Scientific Computing
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We investigate two-level preconditioners on the extended linear system arising from the domain decomposition method. The additive Schwarz method is used as a smoother, and the coarse grid space is constructed by using the Ritz vectors obtained in the Arnoldi process. The coarse grid space can be improved adaptively as the Ritz vectors become a better approximation of the eigenvectors. Numerical tests on the model problem demonstrate the efficiency.