A Framework for Studying the Regularizing Properties of Krylov Subspace Methods

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. CGLS, for which a theoretical analysis is available, is taken as reference method. Tools for measuring the regularization efficiency and the consistency with the discrepancy principle are introduced. An extensive experimentation validates the proposed measures for the studied methods.