The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore the use of fractional powers of the matrices {Mathematical expression} (for Tikhonov regularization) and A (for Lavrentiev regularization) as regularization matrices, where A is the matrix that defines the linear discrete ill-posed problem. Both small- and large-scale problems are considered. © 2013 Springer Science+Business Media Dordrecht.

Fractional regularization matrices for linear discrete ill-posed problems / Michiel E., Hochstenbach; Noschese, Silvia; Lothar, Reichel. - In: JOURNAL OF ENGINEERING MATHEMATICS. - ISSN 0022-0833. - STAMPA. - 93:(2015), pp. 1-113. [10.1007/s10665-013-9671-4]

Fractional regularization matrices for linear discrete ill-posed problems

NOSCHESE, Silvia;
2015

Abstract

The numerical solution of linear discrete ill-posed problems typically requires regularization. Two of the most popular regularization methods are due to Tikhonov and Lavrentiev. These methods require the choice of a regularization matrix. Common choices include the identity matrix and finite difference approximations of a derivative operator. It is the purpose of the present paper to explore the use of fractional powers of the matrices {Mathematical expression} (for Tikhonov regularization) and A (for Lavrentiev regularization) as regularization matrices, where A is the matrix that defines the linear discrete ill-posed problem. Both small- and large-scale problems are considered. © 2013 Springer Science+Business Media Dordrecht.
2015
fractional power regularization matrix; ill-posed problem; fractional tikhonov regularization; fractional lavrentiev regularization
01 Pubblicazione su rivista::01a Articolo in rivista
Fractional regularization matrices for linear discrete ill-posed problems / Michiel E., Hochstenbach; Noschese, Silvia; Lothar, Reichel. - In: JOURNAL OF ENGINEERING MATHEMATICS. - ISSN 0022-0833. - STAMPA. - 93:(2015), pp. 1-113. [10.1007/s10665-013-9671-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/532053
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