@TECHREPORT\{IMM2006-04504,
    author       = "T. K. Jensen and P. C. Hansen",
    title        = "Iterative regularization with minimum-residual methods",
    year         = "2006",
    keywords     = "Iterative regularization, discrete ill-posed problems, {GMRES,} {RRGMRES,} {MINRES,} {MR-II,} Krylov subspaces",
    number       = "",
    series       = "IMM-Technical Report-2006-04",
    institution  = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/4504-full.html",
    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."
}