Iterative regularization with minimum-residual methods |
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Authors: | TK Jensen PC Hansen |
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Institution: | (1) TNM Consult, Marielundvej 48, DK-2730 Herlev, Denmark;(2) Informatics and Mathematical Modelling, Technical University of Denmark, Building 321, DK-2800 Lyngby, Denmark |
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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.
AMS subject classification (2000) 65F22, 65F10 |
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Keywords: | iterative regularization discrete ill-posed problems GMRES RRGMRES MINRES MR-II Krylov subspaces |
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