Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems

  title={Right-Hand Side Dependent Bounds for GMRES Applied to Ill-Posed Problems},
  author={Jennifer Pestana},
  booktitle={System Modelling and Optimization},
  • J. Pestana
  • Published in
    System Modelling and…
    9 September 2013
  • Mathematics, Computer Science
In this paper we apply simple GMRES bounds to the nearly singular systems that arise in ill-posed problems. Our bounds depend on the eigenvalues of the coefficient matrix, the right-hand side vector and the nonnormality of the system. The bounds show that GMRES residuals initially decrease, as residual components associated with large eigenvalues are reduced, after which semi-convergence can be expected because of the effects of small eigenvalues. 



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