Iterative Regularization with Minimum-Residual Methods

Toke Koldborg Jensen, Per Christian Hansen

    Research output: Contribution to journalJournal articleResearchpeer-review

    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.
    Original languageEnglish
    JournalBIT Numerical Mathematics
    Volume47
    Issue number1
    Pages (from-to)103-120
    ISSN0006-3835
    DOIs
    Publication statusPublished - 2007

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