Matrix analysis
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific and Statistical Computing
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
An iterative method for nonsymmetric systems with multiple right-hand sides
SIAM Journal on Scientific Computing
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
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
SIAM Journal on Scientific Computing
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Look-Ahead Procedures for Lanczos-Type Product Methods Based on Three-Term Lanczos Recurrences
SIAM Journal on Matrix Analysis and Applications
A Lanczos-type method for multiple starting vectors
Mathematics of Computation
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
Convergence of Restarted Krylov Subspaces to Invariant Subspaces
SIAM Journal on Matrix Analysis and Applications
A Technique for Accelerating the Convergence of Restarted GMRES
SIAM Journal on Matrix Analysis and Applications
The Lanczos and Conjugate Gradient Algorithms: From Theory to Finite Precision Computations (Software, Environments, and Tools)
Recycling Krylov Subspaces for Sequences of Linear Systems
SIAM Journal on Scientific Computing
Spectral Graph Theory and its Applications
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Restarted block-GMRES with deflation of eigenvalues
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
The Arnoldi Eigenvalue Iteration with Exact Shifts Can Fail
SIAM Journal on Matrix Analysis and Applications
A Useful Form of Unitary Matrix Obtained from Any Sequence of Unit 2-Norm $n$-Vectors
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
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A restarted nonsymmetric Lanczos algorithm is given for computing eigenvalues and both right and left eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Restarting also makes it possible to deal with roundoff error in new ways. We give a scheme for avoiding near-breakdown and discuss maintaining biorthogonality. A system of linear equations can be solved simultaneously with the eigenvalue computations. Deflation from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. The right and left eigenvectors generated while solving the linear equations can be used to help solve systems with multiple right-hand sides.