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Perturbation bounds for polynomials

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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).

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  1. A. Galántai

    Present address: Budapest Tech, John von Neumann Faculty of Informatics, Bécsi út 96/b, 1034, Budapest, Hungary

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  1. University of Miskolc, 3515, Miskolc, Hungary

    A. Galántai

  2. Eötvös Loránd University, Pázmány Péter sétány 1/c, 1117, Budapest, Hungary

    C. J. Hegedűs

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Galántai, A., Hegedűs, C.J. Perturbation bounds for polynomials. Numer. Math. 109, 77–100 (2008). https://doi.org/10.1007/s00211-007-0124-8

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