Characterizations of the Optimal Descartes' Rules of Signs
作者:
J. M. Carnicer,
J. M. Peña,
期刊:
Mathematische Nachrichten
(WILEY Available online 1998)
卷期:
Volume 189,
issue 1
页码: 33-48
ISSN:0025-584X
年代: 1998
DOI:10.1002/mana.19981890104
出版商: WILEY‐VCH Verlag
关键词: Descartes' rule of signs;zeros of functions;Tchebycheff systems;total positivity.
数据来源: WILEY
摘要:
AbstractA 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 functions satisfying a stronger property than the above mentioned Descartes' rule: The difference between the number of zeros and the changes of sign in the sequence of coefficients must be always a nonnegative even number. We show that the approximation to the number of zeros given by these systems of functions is better than the approximation provided by any other systems of functions satisfying a Descartes' rule of signs. This last result improves, in the particular case of polynomials, the main theorem of [14].
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