Abstract
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.
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