Geodesic
Vincent's theorem of~1836: overview and future research
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 5-33

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we present the two different versions of Vincent's theorem of 1836 and discuss the 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. Bibl. – 45 titles. 
@article{ZNSL_2009_373_a0,
     author = {A. G. Akritas},
     title = {Vincent's theorem of~1836: overview and future research},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--33},
     publisher = {mathdoc},
     volume = {373},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a0/}
}
TY  - JOUR
AU  - A. G. Akritas
TI  - Vincent's theorem of~1836: overview and future research
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2009
SP  - 5
EP  - 33
VL  - 373
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a0/
LA  - en
ID  - ZNSL_2009_373_a0
ER  - 
%0 Journal Article
%A A. G. Akritas
%T Vincent's theorem of~1836: overview and future research
%J Zapiski Nauchnykh Seminarov POMI
%D 2009
%P 5-33
%V 373
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a0/
%G en
%F ZNSL_2009_373_a0
A. G. Akritas. Vincent's theorem of~1836: overview and future research. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 5-33. http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a0/