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On the regularizing properties of the GMRES method

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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.

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Authors and Affiliations

  1. Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA; e-mail: dxc57@po.cwru.edu , , , , , , US

    D. Calvetti

  2. Department of Mathematics and Computer Science, Kent State University, Kent, OH 44242, USA; e-mail: {blewis,reichel}@mcs.kent.edu , , , , , , US

    B. Lewis & L. Reichel

Authors
  1. D. Calvetti
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  2. B. Lewis
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  3. L. Reichel
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Additional information

Received November 10, 2000 / Revised version received April 11, 2001 / Published online October 17, 2001

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Calvetti, D., Lewis, B. & Reichel, L. On the regularizing properties of the GMRES method. Numer. Math. 91, 605–625 (2002). https://doi.org/10.1007/s002110100339

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  • DOI: https://doi.org/10.1007/s002110100339

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