@COMMENT {Autogenerated file by bib2html.pl version 0.94}
@InProceedings{mmt-mcf-snc-2009,
author = {Angelos Mantzaflaris and Bernard Mourrain and Elias
P. Tsigaridas},
title = {Continued fraction expansion of real roots of
polynomial systems},
booktitle = SNC_2009,
year = 2009,
isbn = {978-1-60558-664-9},
pages = {85--94},
address = {Kyoto, Japan},
publisher = {ACM},
editor = {H. Kai and H. Sekigawa},
abstract = " We present a new algorithm for isolating the real
roots of a system of multivariate polynomials, given
in the \emph{monomial basis}. It is inspired by
existing subdivision methods in the Bernstein basis;
it can be seen as generalization of the univariate
continued fraction algorithm or alternatively as a
fully analog of Bernstein subdivision in the
monomial basis. The representation of the
subdivided domains is done through
\emph{homographies}, which allows us to use only
integer arithmetic and to treat efficiently
unbounded regions. We use univariate bounding
functions, projection and preconditioning techniques
to reduce the domain of search. The resulting boxes
have optimized rational coordinates, corresponding
to the first terms of the \emph{continued fraction
expansion} of the real roots. An extension of
\emph{Vincent's Theorem} to multivariate polynomials
is established and used to prove termination of the
algorithm. New complexity bounds are provided for a
simplified version of the algorithm. Examples
computed with our C++ implementation illustrate the
approach.",
}