Geodesic
Topological complexity and real roots of polynomials
Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 670-680.

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

The topological complexity of an algorithm is the number of its branchings. In the paper we prove that the minimal topological complexity of an algorithm that approximately computes a root of a real polynomial of degree $d$ equals $d/2$ for even $d$, is greater than or equal to 1 for odd $d>-3$, and equals 1 for $d=3$ or 5. 
@article{MZM_1996_60_5_a2,
     author = {V. A. Vassiliev},
     title = {Topological complexity and real roots of polynomials},
     journal = {Matemati\v{c}eskie zametki},
     pages = {670--680},
     publisher = {mathdoc},
     volume = {60},
     number = {5},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a2/}
}
TY  - JOUR
AU  - V. A. Vassiliev
TI  - Topological complexity and real roots of polynomials
JO  - Matematičeskie zametki
PY  - 1996
SP  - 670
EP  - 680
VL  - 60
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a2/
LA  - ru
ID  - MZM_1996_60_5_a2
ER  - 
%0 Journal Article
%A V. A. Vassiliev
%T Topological complexity and real roots of polynomials
%J Matematičeskie zametki
%D 1996
%P 670-680
%V 60
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a2/
%G ru
%F MZM_1996_60_5_a2
V. A. Vassiliev. Topological complexity and real roots of polynomials. Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 670-680. http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a2/

[1] Smale S., “On the topology of algorithms, I”, J. Complex, 3 (1987), 81–89 | DOI | MR | Zbl

[2] Vasilev V. A., “Kogomologii grupp kos i slozhnost algoritmov”, Funktsion. analiz i ego prilozh., 22:3 (1988), 15–24 | MR | Zbl

[3] Vasilev V. A., “Topologicheskaya slozhnost algoritmov priblizhennogo resheniya sistem polinomialnykh uravnenii”, Algebra i analiz, 1:6 (1989), 98–113 | MR | Zbl

[4] Vassiliev V. A., Complements of Discriminants of Smooth Maps: Topology and Applications, Revised edition, Translations of Math. Monographs, 98, AMS, Providence, 1994