On the regularizing properties of the GMRES method

@article{Calvetti2002OnTR,
  title={On the regularizing properties of the GMRES method},
  author={Daniela Calvetti and Bryan Lewis and Lothar Reichel},
  journal={Numerische Mathematik},
  year={2002},
  volume={91},
  pages={605-625}
}
The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. However, little is known about the behavior of this method when it is applied to the solution of nonsymmetric linear ill-posed problems with a right-hand side that is contaminated by errors. We show that when the associated error-free right-hand side lies in a finite-dimensional Krylov subspace, the GMRES method is a regularization method. The iterations… CONTINUE READING

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