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Numerische Mathematik

, Volume 109, Issue 1, pp 77–100 | Cite as

Perturbation bounds for polynomials

  • A. GalántaiEmail author
  • C. J. Hegedűs
Article

Abstract

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 result of Edelman and Murakami (Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, SIAM, Philapdelphia, 1994; Math Comput 64:210–763, 1995).

Mathematics Subject Classification (2000)

65H05 65F15 65F35 15A42 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.University of MiskolcMiskolcHungary
  2. 2.Budapest Tech, John von Neumann Faculty of InformaticsBudapestHungary
  3. 3.Eötvös Loránd UniversityBudapestHungary

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