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On Descartes' rules of signs and their exactness

✍ Scribed by J. M. Peña

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
143 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

This paper revisits the Descartes' rules of signs and provides new bounds for the number of complex roots of a polynomial in certain complex regions. We also prove that the Descartes' rules associated with the Bernstein basis are exact for polynomials whose roots are real. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Characterizations of the Optimal Descart
Characterizations of the Optimal Descartes' Rules of Signs
✍ J. M. Carnicer; J. M. Peña 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 902 KB

A system of functions satisfies Descartes' rule of signs if the number of zeros (with multiplicities) of a linear combination of these functions is less than or equal to the number of variations of strict sign in the sequence of the coefficients. In this paper we characterize the systems of function