Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method

@article{Knyazev2001TowardTO,
  title={Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method},
  author={A. Knyazev},
  journal={SIAM J. Sci. Comput.},
  year={2001},
  volume={23},
  pages={517-541}
}
  • A. Knyazev
  • Published 2001
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
We describe new algorithms of the locally optimal block preconditioned conjugate gradient (LOBPCG) method for symmetric eigenvalue problems, based on a local optimization of a three-term recurrence, and suggest several other new methods. To be able to compare numerically different methods in the class, with different preconditioners, we propose a common system of model tests, using random preconditioners and initial guesses. As the "ideal" control algorithm, we advocate the standard… Expand
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