On the regularizing properties of the GMRES method

  title={On the regularizing properties of the GMRES method},
  author={Daniela Calvetti and Bryan Lewis and Lothar Reichel},
  journal={Numerische Mathematik},
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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GMRES: a generalized minimal residual method for solving nonsymmetric linear systems

  • Y. Saad, M. H. Schultz
  • SIAM J. Sci. Stat. Comput., 7
  • 1986
Highly Influential
7 Excerpts

The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind

  • C. W. Groetsch
  • Pitman, London
  • 1984
Highly Influential
4 Excerpts

The use of auto-correlation for pseudo-rank determination in noisy ill-conditioned least-squares problems

  • M. L. Baart
  • IMA J. Numer. Anal., 2
  • 1982
Highly Influential
3 Excerpts

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