Error estimates for linear systems with applications to regularization

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.

Trovami (UniCASearch)
Titolo: Error estimates for linear systems with applications to regularization
Autori: 
RODRIGUEZ, GIUSEPPE
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Data di pubblicazione: 2008
Rivista: 
NUMERICAL ALGORITHMS  
Citazione: Error estimates for linear systems with applications to regularization / BREZINSKI C; RODRIGUEZ G; SEATZU S. - 49(2008), pp. 85-104.
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.
Handle: http://hdl.handle.net/11584/16248
Tipologia:1.1 Articolo in rivista

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