Backward stability of polynomial root-finding using Fiedler companion matrices

@article{Tern2014BackwardSO,
  title={Backward stability of polynomial root-finding using Fiedler companion matrices},
  author={F. Ter{\'a}n and F. M. Dopico and J. P{\'e}rez},
  journal={Ima Journal of Numerical Analysis},
  year={2014},
  volume={36},
  pages={133-173}
}
Computing roots of scalar polynomials as the eigenvalues of Frobenius companion matrices using backward stable eigenvalue algorithms is a classical approach. The introduction of new families of companion matrices allows for the use of other matrices in the root-finding problem. In this paper, we analyze the backward stability of polynomial root-finding algorithms via Fiedler companion matrices. In other words, given a polynomial p(z), the question is to determine whether the whole set of… Expand
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