Iterative regularization with minimum-residual methods

Toke Koldborg Jensen, Per Christian Hansen

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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
    Publication statusPublished - 2006

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