Efficient Preconditioned Inner Solves For Inexact Rayleigh Quotient Iteration And Their Connections To The Single-Vector Jacobi-Davidson Method

@article{Szyld2011EfficientPI,
  title={Efficient Preconditioned Inner Solves For Inexact Rayleigh Quotient Iteration And Their Connections To The Single-Vector Jacobi-Davidson Method},
  author={Daniel B. Szyld and Fei Xue},
  journal={SIAM J. Matrix Analysis Applications},
  year={2011},
  volume={32},
  pages={993-1018}
}
We study inexact Rayleigh quotient iteration (IRQI) for computing a simple interior eigenpair of the generalized eigenvalue problem Av 1⁄4 λBv, providing new insights into a special type of preconditioners with “tuning” for the efficient iterative solution of the shifted linear systems that arise in this algorithm. We first give a new convergence analysis of IRQI, showing that locally cubic and quadratic convergence can be achieved for Hermitian and non-Hermitian problems, respectively, if the… CONTINUE READING
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