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Numerische Mathematik

, Volume 91, Issue 4, pp 605–625 | Cite as

On the regularizing properties of the GMRES method

  • D. Calvetti
  • B. Lewis
  • L. Reichel
Original article

Summary.

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 are terminated by a stopping rule based on the discrepancy principle.

Mathematics Subject Classifications: 65F10, 65F22, 65R30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • D. Calvetti
    • 1
  • B. Lewis
    • 2
  • L. Reichel
    • 2
  1. 1.Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA; e-mail: dxc57@po.cwru.edu US
  2. 2.Department of Mathematics and Computer Science, Kent State University, Kent, OH 44242, USA; e-mail: {blewis,reichel}@mcs.kent.edu US

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