Filter factor analysis of an iterative multilevel regularizing method

Recent results have shown that iterative methods of multigrid type are very precise and efficient for regularizing purposes: the reconstruction quality is of the same level or slightly better than that related to most effective regularizing procedures such as Landweber or conjugate gradients for nor...

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Bibliographic Details
Published inElectronic transactions on numerical analysis Vol. 29; p. 163
Main Authors Donatelli, Marco, Serra-Capizzano, Stefano
Format Journal Article
LanguageEnglish
Published Institute of Computational Mathematics 01.12.2007
Subjects
Boundary value problems
Evaluation
Iterative methods (Mathematics)
Matrices
Methods
Properties
Italy
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ISSN1068-9613
1097-4067

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Summary:Recent results have shown that iterative methods of multigrid type are very precise and efficient for regularizing purposes: the reconstruction quality is of the same level or slightly better than that related to most effective regularizing procedures such as Landweber or conjugate gradients for normal equations, but the associated computational cost is highly reduced. Here we analyze the filter features of one of these multigrid techniques in order to provide a theoretical motivation of the excellent regularizing characteristics experimentally observed in the discussed methods. Key words. regularization, early termination, filter analysis, boundary conditions, structured matrices AMS subject classifications. 65Y20, 65F10, 15A12
ISSN:1068-9613
1097-4067