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Vincent’s theorem of 1836: overview and future research

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In this paper, we present two different versions of Vincent’s theorem of 1836 and discuss various real root isolation methods derived from them: one using continued fractions and two using bisections, the former being the fastest real root isolation method. Regarding the continued fractions method, we first show how, using a recently developed quadratic complexity bound on the values of the positive roots of polynomials, its performance has been improved by an average of 40% over its initial implementation, and then we indicate directions for future research. Bibliography: 45 titles.

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Authors and Affiliations

  1. Department of Computer and Communication, Engineering University of Thessaly, Thessaly, Greece

    A. G. Akritas

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Correspondence to A. G. Akritas.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 373, 2009, pp. 5–33.

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Akritas, A.G. Vincent’s theorem of 1836: overview and future research. J Math Sci 168, 309–325 (2010). https://doi.org/10.1007/s10958-010-9982-1

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