Iterative regularization with minimum-residual methods | Toke Koldborg Jensen, Per Christian Hansen
| | 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. | | Keywords | Iterative regularization, discrete ill-posed problems, GMRES, RRGMRES, MINRES, MR-II, Krylov subspaces | | Type | Technical report | | Year | 2006 | | Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU | | Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby | | Series | IMM-Technical Report-2006-04 | | Electronic version(s) | [pdf] | | BibTeX data | [bibtex] | | IMM Group(s) | Scientific Computing |
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