GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Journal of Computational and Applied Mathematics
Deflation of conjugate gradients with applications to boundary value problems
SIAM Journal on Numerical Analysis
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Quasi-kernel polynomials and their use in non-Hermitian matrix iterations
Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
An iterative method for nonsymmetric systems with multiple right-hand sides
SIAM Journal on Scientific Computing
SIAM Journal on Matrix Analysis and Applications
A Restarted GMRES Method Augmented with Eigenvectors
SIAM Journal on Matrix Analysis and Applications
A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides
Proceedings of the 6th international congress on Computational and applied mathematics
On restarting the Arnoldi method for large nonsymmetric eigenvalue problems
Mathematics of Computation
Restarted GMRES preconditioned by deflation
Journal of Computational and Applied Mathematics
Analysis of Augmented Krylov Subspace Methods
SIAM Journal on Matrix Analysis and Applications
Analysis of Projection Methods for Solving Linear Systems with Multiple Right-Hand Sides
SIAM Journal on Scientific Computing
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Adaptively Preconditioned GMRES Algorithms
SIAM Journal on Scientific Computing
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
SIAM Journal on Matrix Analysis and Applications
Matrix algorithms
SIAM Journal on Scientific Computing
GMRES with Deflated Restarting
SIAM Journal on Scientific Computing
A Krylov--Schur Algorithm for Large Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Truncation Strategies for Optimal Krylov Subspace Methods
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Analyses of the lanczos algorithm and of the approximation problem in richardson's method
Analyses of the lanczos algorithm and of the approximation problem in richardson's method
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Improving the Accuracy of GMRes with Deflated Restarting
SIAM Journal on Scientific Computing
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
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A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is necessary to control roundoff error, and several approaches are discussed. The eigenvectors generated while solving the linear equations can be used to help solve systems with multiple right-hand sides. Experiments are given with large matrices from quantum chromodynamics that have many right-hand sides.