Géométrie des polynômes. Coût global moyen de la méthode de Newton
Séminaire Bourbaki (1986-1987)
- Volume: 29, page 19-36
- ISSN: 0303-1179
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topMarin, Alexis. "Géométrie des polynômes. Coût global moyen de la méthode de Newton." Séminaire Bourbaki 29 (1986-1987): 19-36. <http://eudml.org/doc/110079>.
@article{Marin1986-1987,
author = {Marin, Alexis},
journal = {Séminaire Bourbaki},
keywords = {computational efficiency; Newton's method; polynomial equations},
language = {fre},
pages = {19-36},
publisher = {Société Mathématique de France},
title = {Géométrie des polynômes. Coût global moyen de la méthode de Newton},
url = {http://eudml.org/doc/110079},
volume = {29},
year = {1986-1987},
}
TY - JOUR
AU - Marin, Alexis
TI - Géométrie des polynômes. Coût global moyen de la méthode de Newton
JO - Séminaire Bourbaki
PY - 1986-1987
PB - Société Mathématique de France
VL - 29
SP - 19
EP - 36
LA - fre
KW - computational efficiency; Newton's method; polynomial equations
UR - http://eudml.org/doc/110079
ER -
References
top- [Ba] B. Barna, Uber Divergenzpunkte des Newtonshe Verfahrens zur Bestimmung von Würzeln algebraischer Gleichungen III, Publ. Math. Debrecen8 (1961), 193-207. Zbl0189.48002MR135224
- [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. Zbl0587.30028MR816367
- [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). Zbl0634.30006MR923552
- [G] O. Gabber, Diverses interventions au Séminaire Bourbaki, tradition orale.
- [H] W. Hayman, "Multivalent functions", Cambridge Univ. Press, Cambridge, 1958. Zbl0904.30001MR108586
- [HPS] M. Hirsch, C. Pugh AND M. Shub, Invariant manifolds, Lectures Notes in Math.583 (1977), Springer, New-York. Zbl0355.58009MR501173
- [HM] M. Hurley AND C. Martin, Newton's algorithm and chaotic dynamical systems, SIAM J. Math. Anal.15 (1984), 238-252. Zbl0588.65033MR731865
- [Ka] L. Kantorovitch ET G. Akilov, Analyse fonctionnelle, t.2, Editions MIR, Moscou, 1981. Zbl0531.46001
- [McM] C. McMullen, "Families of Rationals Maps and Iterative Root-Finding Algorithms", Ph. D., Harvard Univ., Mai 1985, à paraître. Zbl0634.30028
- [M] A. Marin, Les arbres de Shub-Smale, Séminaire de Géométrie algébrique réelle ( J.J. Risler), Publ. Univ. Paris VII24 (1986). MR923553
- [O] J. Oesterle, Démonstration de la conjecture de Bieberbach, exposé n°649 du Séminaire Bourbaki (juin 1985). Zbl0625.30019
- [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. Zbl0618.65038
- [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. Monthly91 (1984), 3-17. Zbl0532.58016MR729188
- [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. Computing15 (1986), 145-161. Zbl0625.65036MR822199
- [ShSm3] M. Shub AND S. Smale, On the existence of generally convergent algorithms, Jour. of Complexity2 (1986), 2-11. Zbl0595.65048MR925341
- [STW] M. Shub, D. Tischler AND R. Williams, The Newtonian graph of a complex polynomial, soumis à SIAM J. of Math. Analysis. Zbl0653.58013MR924558
- [Sm1] S. Smale, A Convergent process of price adjustment and global Newton methods, J. Math. Econom.3 (1976), 107-120. Zbl0354.90018MR411577
- [Sm2] S. Smale, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc.4 (1981), 107-120. Zbl0456.12012MR590817
- [Sm3] S. Smale, The Problem of the average speed of the simplex method, in "Mathematical Programming: the state of the Art", Bonn1982 (editors Bachem et al.), Springer, 1983. Zbl0552.90059MR717413
- [Sm4] S. Smale, On the efficiency of algorithms of analysis, Bull. Amer. Math. Soc.13 (1985), 87-121. Zbl0592.65032MR799791
- [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, SpringerNew York (1986). Zbl0613.65058MR870648
- [Sm6] S. Smale, Algorithms for solving equations, MSRI Berkeley, 1986 (texte écrit pour le congrès mondial de Berkeley). Zbl0665.65058MR934223
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