Restarted Simpler GMRES Augmented with Harmonic Ritz Vectors

  • Ravindra Boojhawon
  • Muddun Bhuruth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2330)


We describe a method for improving the convergence of the Simpler GMRES method for problems with small eigenvalues. We augment the Krylov subspace with harmonic Ritz vectors corresponding to the smallest harmonic Ritz values. The advantage over augmented GMRES is that the problem of finding the minimal residual solution reduces to an upper triangular least-squares problem instead of an upper-Hessenberg least-squares problem. A second advantage is that harmonic Ritz pairs can be cheaply computed. Numerical tests indicate that augmented Simpler GMRES(m) is superior to Simpler GMRES(m) and requires a lesser amount of work than augmented GMRES(m).


Small Eigenvalue Krylov Subspace Residual Norm Convergence History GMRES Method 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ravindra Boojhawon
    • 1
  • Muddun Bhuruth
    • 1
  1. 1.Department of MathematicsUniversity of MauritiusReduitMauritius

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