Iterative Regularization with Minimum-Residual Methods

Publication: Research - peer-reviewJournal article – Annual report year: 2007

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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.
Original languageEnglish
JournalBIT Numerical Mathematics
Volume47
Issue number1
Pages (from-to)103-120
ISSN0006-3835
DOIs
StatePublished - 2007
Peer-reviewedYes
CitationsWeb of Science® Times Cited: 20
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