Matrix analysis
The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems
SIAM Journal on Matrix Analysis and Applications
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
Iterative methods for solving linear systems
Iterative methods for solving linear systems
The symmetric eigenvalue problem
The symmetric eigenvalue problem
An analysis of the Rayleigh—Ritz method for approximating eigenspaces
Mathematics of Computation
Matrix algorithms
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Iterative methods for large, sparse, nonsymmetric systems of linear equations
Iterative methods for large, sparse, nonsymmetric systems of linear equations
Convergence of Restarted Krylov Subspaces to Invariant Subspaces
SIAM Journal on Matrix Analysis and Applications
Some Remarks on the Elman Estimate for GMRES
SIAM Journal on Matrix Analysis and Applications
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This paper takes another look at the convergence analysis of the Arnoldi procedure for solving non-Hermitian eigenvalue problems. Two main viewpoints are put in contrast. The first exploits the eigenbasis, when there is one, and relies on classical min-max approximation theory results. The second approach relies on the Schur factorization. Its aim is to link the convergence analysis of the Arnoldi process for eigenvalue problems to that of the generalized minimal residual iterations (GMRES), for which much is known.