Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems

@article{Szyld2013LocalCA,
  title={Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems},
  author={Daniel B. Szyld and Fei Xue},
  journal={Numerische Mathematik},
  year={2013},
  volume={123},
  pages={333-362}
}
We study the local convergence of several inexact numerical algorithms closely related to Newton’s method for the solution of a simple eigenpair of the general nonlinear eigenvalue problem T (λ)v = 0. We investigate inverse iteration, Rayleigh quotient iteration, residual inverse iteration, and the single-vector Jacobi–Davidson method, analyzing the impact of the tolerances chosen for the approximate solution of the linear systems arising in these algorithms on the order of the local… CONTINUE READING

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