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Numerical Linear Algebra with Applications
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Numerical Linear Algebra with Applications
Article . 2012 . Peer-reviewed
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Square regularization matrices for large linear discrete ill‐posed problems

Square regularization matrices for large linear discrete ill-posed problems.
descriptionPublicationkeyboard_double_arrow_right Article 23 Apr 2012 Italy English Publisher:WileyJournal:Numerical Linear Algebra with Applications, volume 19, pages 896-913 (issn: 1070-5325, eissn: 1099-1506, Copyright policy )
Authors: DONATELLI, MARCO; Neuman A.; Reichel L.;

doi: 10.1002/nla.1833

handle: 11383/1758469

Square regularization matrices for large linear discrete ill‐posed problems

Abstract

SUMMARYLarge linear discrete ill‐posed problems with contaminated data are often solved with the aid of Tikhonov regularization. Commonly used regularization matrices are finite difference approximations of a suitable derivative and are rectangular. This paper discusses the design of square regularization matrices that can be used in iterative methods based on the Arnoldi process for large‐scale Tikhonov regularization problems. Copyright © 2012 John Wiley & Sons, Ltd.

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Italy
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Keywords

Finite difference methods for boundary value problems involving PDEs, Iterative numerical methods for linear systems, Numerical solutions to overdetermined systems, pseudoinverses, Tikhonov regularization, Arnoldi process, smoothing operators, ill-posed problem, pseudoinverse, finite difference matrices, Ill-posedness and regularization problems in numerical linear algebra, regularization operator, numerical experiments, range restricted GMRES

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
32
Top 10%
Top 10%
Top 10%
bronze