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Summary: Journal of Mathematical Sciences, Vol. 168, No. 3, 2010
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.
1. Introduction
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