Iterative regularization with minimum-residual methods

Abstract We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these...
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Autor*in:	Jensen, T.K. [verfasserIn] Hansen, P.C.

Format:	Artikel
Sprache:	Englisch

Erschienen:	2007

Anmerkung:	© Springer Science + Business Media B.V. 2007

Übergeordnetes Werk:	Enthalten in: BIT - Kluwer Academic Publishers, 1961, 47(2007), 1 vom: 20. Jan., Seite 103-120
Übergeordnetes Werk:	volume:47 ; year:2007 ; number:1 ; day:20 ; month:01 ; pages:103-120

Links:	Volltext

DOI / URN:	10.1007/s10543-006-0109-5

Katalog-ID:	OLC2050629370

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title	Iterative regularization with minimum-residual methods
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title_full	Iterative regularization with minimum-residual methods
author_sort	Jensen, T.K.
journal	BIT
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lang_code	eng
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container_start_page	103
author_browse	Jensen, T.K. Hansen, P.C.
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author-letter	Jensen, T.K.
doi_str_mv	10.1007/s10543-006-0109-5
dewey-full	070
title_sort	iterative regularization with minimum-residual methods
title_auth	Iterative regularization with minimum-residual methods
abstract	Abstract We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES – their success as regularization methods is highly problem dependent. © Springer Science + Business Media B.V. 2007
abstractGer	Abstract We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES – their success as regularization methods is highly problem dependent. © Springer Science + Business Media B.V. 2007
abstract_unstemmed	Abstract We study the regularization properties of iterative minimum-residual methods applied to discrete ill-posed problems. In these methods, the projection onto the underlying Krylov subspace acts as a regularizer, and the emphasis of this work is on the role played by the basis vectors of these Krylov subspaces. We provide a combination of theory and numerical examples, and our analysis confirms the experience that MINRES and MR-II can work as general regularization methods. We also demonstrate theoretically and experimentally that the same is not true, in general, for GMRES and RRGMRES – their success as regularization methods is highly problem dependent. © Springer Science + Business Media B.V. 2007
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container_issue	1
title_short	Iterative regularization with minimum-residual methods
url	https://doi.org/10.1007/s10543-006-0109-5
remote_bool	false
author2	Hansen, P.C.
author2Str	Hansen, P.C.
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doi_str	10.1007/s10543-006-0109-5
up_date	2024-07-04T02:26:35.980Z
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