In this paper, we discuss several (old and new) estimates for the norm of the error in the solution of systems of linear equations, and we study their properties. Then, these estimates are used for approximating the optimal value of the regularization parameter in Tikhonov’s method for illconditioned systems. They are also used as a stopping criterion in iterative methods, such as the conjugate gradient algorithm, which have a regularizing effect. Several numerical experiments and comparisons with other procedures show the effectiveness of our estimates.

Error estimates for linear systems with applications to regularization / BREZINSKI C; RODRIGUEZ G; SEATZU S. - 49(2008), pp. 85-104.

Error estimates for linear systems with applications to regularization

RODRIGUEZ, GIUSEPPE;
2008

Abstract

In this paper, we discuss several (old and new) estimates for the norm of the error in the solution of systems of linear equations, and we study their properties. Then, these estimates are used for approximating the optimal value of the regularization parameter in Tikhonov’s method for illconditioned systems. They are also used as a stopping criterion in iterative methods, such as the conjugate gradient algorithm, which have a regularizing effect. Several numerical experiments and comparisons with other procedures show the effectiveness of our estimates.
Ill-conditioned linear systems; Regularization; Error estimates
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11584/16248
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