Istituto di Matematica Applicata e Tecnologie Informatiche     
Simoncini V. On the convergence of restarted Krylov subspace methods. Preprint ercim.cnr.ian//1998-1093, 1998.
Given the large linear system of equations begin{eqnarray}label{eqn:main} Ax=b, quadmbox{ with } quad AinRR^{ntimes n}, ; binRR^n, end{eqnarray} we are interested in the convergence analysis of restarted Krylov subspace iterative solvers for nref{eqn:main}. Classical results associate the convergence behavior to some spectral properties of the coefficient matrix. In particular, eigenvalues close to the origin may strongly affect the performance of the methods. More recently, pseudospectrum has been shown to be useful in evaluating asymptotic convergence, while harmonic Ritz values have been used to improve the convergence performance.
Subject Krylov subspace methods

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