Géométrie des polynômes. Coût global moyen de la méthode de Newton
Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque, no. 152-153 (1987), Exposé no. 670, 18 p. 
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     title = {G\'eom\'etrie des polyn\^omes. {Co\^ut} global moyen de la m\'ethode de {Newton}},
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Marin, Alexis. Géométrie des polynômes. Coût global moyen de la méthode de Newton, dans Séminaire Bourbaki : volume 1986/87, exposés 669-685, Astérisque, no. 152-153 (1987), Exposé no. 670, 18 p. http://archive.numdam.org/item/SB_1986-1987__29__19_0/

[Ba] B. Barna, Uber Divergenzpunkte des Newtonshe Verfahrens zur Bestimmung von Würzeln algebraischer Gleichungen III, Publ. Math. Debrecen 8 (1961), 193-207. | MR 135224 | Zbl 0189.48002

[C] J. Curry, On zero finding methods of higher order from data at one point, MSRI Berkeley (1986).

[DH] A. Douady AND J. H. Hubbard, On the dynamics of polynomial like mappings, Ann. Sci. E.N.S., 4e série, t.18 (1985), 287-343. | Numdam | MR 816367 | Zbl 0587.30028

[F] J.-P. Francoise, Estimations uniformes pour les domaines de convergence de la méthode de Newton, Séminaire de Géométrie Algébrique Réelle (J. J. Risler), Publ. Univ. Paris VII, 24 (1986). | MR 923552 | Zbl 0634.30006

[G] O. Gabber, Diverses interventions au Séminaire Bourbaki, tradition orale.

[H] W. Hayman, "Multivalent functions", Cambridge Univ. Press, Cambridge, 1958. | MR 108586 | Zbl 0904.30001

[HPS] M. Hirsch, C. Pugh AND M. Shub, Invariant manifolds, Lectures Notes in Math. 583 (1977), Springer, New-York. | MR 501173 | Zbl 0355.58009

[HM] M. Hurley AND C. Martin, Newton's algorithm and chaotic dynamical systems, SIAM J. Math. Anal. 15 (1984), 238-252. | MR 731865 | Zbl 0588.65033

[Ka] L. Kantorovitch ET G. Akilov, Analyse fonctionnelle, t.2, Editions MIR, Moscou, 1981. | Zbl 0531.46001

[McM] C. Mcmullen, "Families of Rationals Maps and Iterative Root-Finding Algorithms", Ph. D., Harvard Univ., Mai 1985, à paraître. | Zbl 0634.30028

[M] A. Marin, Les arbres de Shub-Smale, Séminaire de Géométrie algébrique réelle (J. J. Risler), Publ. Univ. Paris VII 24 (1986). | MR 923553

[O] J. Oesterle, Démonstration de la conjecture de Bieberbach, exposé n°649 du Séminaire Bourbaki (juin 1985). | Numdam | Zbl 0625.30019

[R1] J. Renegar, On the efficiency of Newton's method in approximating all zeros of a system of complex polynomials, à paraître dans Mathematics of Operations Research. | Zbl 0618.65038

[R2] J. Renegar, A polynomial-time algorithm based on Newton's method for linear programming, MSRI Berkeley (1986).

[SU] D. Saari AND J. Urenko, Newton's method, circle maps and chaotic motions, Amer. Math. Monthly 91 (1984), 3-17. | MR 729188 | Zbl 0532.58016

[Sh] M. Shub, The geometry and topology of dynamical systems, and algorithms for numerical problems, notes préparées pour des conférences données à D.D.A, Université de Peking, Bejing, Chine, Août-Septembre 1983.

[ShSm1&2] M. Shub AND S. Smale, Computational complexity on the geometry of polynomials and a theory of cost, PartI, Ann. Sci. E.N.S. (4) t.18 (1985), 107-161; Part II, SIAM J. Computing 15 (1986), 145-161. | MR 822199 | Zbl 0625.65036

[ShSm3] M. Shub AND S. Smale, On the existence of generally convergent algorithms, Jour. of Complexity 2 (1986), 2-11. | MR 925341 | Zbl 0595.65048

[STW] M. Shub, D. Tischler AND R. Williams, The Newtonian graph of a complex polynomial, soumis à SIAM J. of Math. Analysis. | MR 924558 | Zbl 0653.58013

[Sm1] S. Smale, A Convergent process of price adjustment and global Newton methods, J. Math. Econom. 3 (1976), 107-120. | MR 411577 | Zbl 0354.90018

[Sm2] S. Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. 4 (1981), 107-120. | MR 590817 | Zbl 0456.12012

[Sm3] S. Smale, The Problem of the average speed of the simplex method, in "Mathematical Programming: the state of the Art", Bonn 1982 (editors Bachem et al.), Springer, 1983. | MR 717413 | Zbl 0552.90059

[Sm4] S. Smale, On the efficiency of algorithms of analysis, Bull. Amer. Math. Soc. 13 (1985), 87-121. | MR 799791 | Zbl 0592.65032

[Sm5] S. Smale, Newton's method estimates from data at one point, à paraître dans: Proceedings of a Conference at Laramie in Honor of Gail S. Young, Springer New York (1986). | MR 870648 | Zbl 0613.65058

[Sm6] S. Smale, Algorithms for solving equations, MSRI Berkeley, 1986 (texte écrit pour le congrès mondial de Berkeley). | MR 934223 | Zbl 0665.65058