The Ehrlich-Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue Problem

@article{Bini2005TheEM,
  title={The Ehrlich-Aberth Method for the Nonsymmetric Tridiagonal Eigenvalue Problem},
  author={Dario Bini and Luca Gemignani and Françoise Tisseur},
  journal={SIAM J. Matrix Analysis Applications},
  year={2005},
  volume={27},
  pages={153-175}
}
An algorithm based on the Ehrlich–Aberth iteration is presented for the computation of the zeros of p(λ) = det(T−λI), where T is a real irreducible nonsymmetric tridiagonal matrix. The algorithm requires the evaluation of p(λ)/p′(λ) = −1/trace(T − λI)−1, which is done by exploiting the QR factorization of T − λI and the semiseparable structure of (T − λI)−1. The choice of initial approximations relies on a divide-and-conquer strategy, and some results motivating this strategy are given… CONTINUE READING
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