Perturbation bounds for polynomials

@article{Galntai2008PerturbationBF,
  title={Perturbation bounds for polynomials},
  author={Aur{\'e}l Gal{\'a}ntai and Csaba J. Heged{\"u}s},
  journal={Numerische Mathematik},
  year={2008},
  volume={109},
  pages={77-100}
}
Using two different elementary approaches we derive a global and a local perturbation theorem on polynomial zeros that significantly improve the results of Ostrowski (Acta Math 72:99–257, 1940), Elsner et al. (Linear Algebra Appl 142:195–209, 1990). A comparison of different perturbation bounds shows that our results are better in many cases than the similar local result of Beauzamy (Can Math Bull 42(1):3–12, 1999). Using the matrix theoretical approach we also improve the backward stability… CONTINUE READING

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