Istituto di Informatica e Telematica     
Brianzi P., Favati P., Menchi O., Romani F. A framework for studying the regularizing properties of Krylov subspace methods. Technical report, 2004.
Krylov subspace iterative methods have recently received considerable attention as regularizing techniques for solving linear systems with a coefficient matrix of ill-determined rank and a right-hand side vector perturbed by noise. For many of them little is known from this point of view. In this paper the regularizing properties of some methods of Krylov type (CGLS, GMRES, QMR, CGS, BiCG, Bi-CGSTAB) are examined in comparison with other regularization methods (truncated SVD, Tikhonov method, Landweber iteration) for which a complete theoretical analysis is available. Tools for measuring the regularization efficiency are introduced. An extensive experimentation validates the proposed measures on the studied methods. The problem of the choice of the regularization parameter is also addressed by examining the consistency with the discrepancy principle.
Subject Regularization
Ill-posed problem
Krylov subspace method

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