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Reports (Research Report) Year : 2001

Efficient Isolation of a Polynomial Real Roots

Abstract

This paper gives new results for the isolation of real roots of a univariate polynomial using Descartes' rule of signs, following work of Vincent, Uspensky, Collins and Akritas, Johnson, Krandick. The first contribution is a generic algorithm which enables one to describe all the existing strategies in a unified framework. Using that framework, a new algorithm is presented, which is optimal in terms of memory usage, while doing no more computations than other algorithms based on Descartes' rule of signs. We show that these critical optimizations have important consequences by proposing a full efficient solution for isolating the real roots of zero-dimensional polynomial systems.
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Dates and versions

inria-00072518 , version 1 (24-05-2006)

Identifiers

  • HAL Id : inria-00072518 , version 1

Cite

Fabrice Rouillier, Paul Zimmermann. Efficient Isolation of a Polynomial Real Roots. [Research Report] RR-4113, INRIA. 2001. ⟨inria-00072518⟩
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