TY - RPRT
T1 - Iterative regularization with minimum-residual methods
AU - Jensen, Toke Koldborg
AU - Hansen, Per Christian
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
KW - GMRES
KW - Krylov subspaces
KW - MR-II
KW - RRGMRES
KW - MINRES
KW - Iterative regularization
KW - discrete ill-posed problems
M3 - Report
BT - Iterative regularization with minimum-residual methods
ER -