Complexité des méthodes homotopiques pour la résolution des systèmes polynomiaux
Journées Nationales de Calcul Formel. 3 – 7 Mai 2010, Les cours du CIRM, no. 2 (2010), pp. 263-280.
DOI : 10.5802/ccirm.10
Dedieu, Jean-Pierre 1

1 Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31069 Toulouse cedex 9, France
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     title = {Complexit\'e des m\'ethodes homotopiques pour la r\'esolution des syst\`emes polynomiaux},
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Dedieu, Jean-Pierre. Complexité des méthodes homotopiques pour la résolution des systèmes polynomiaux, dans Journées Nationales de Calcul Formel. 3 – 7 Mai 2010, Les cours du CIRM, no. 2 (2010), pp. 263-280. doi : 10.5802/ccirm.10. http://www.numdam.org/articles/10.5802/ccirm.10/

[1] E. Allgower, K. Georg, Numerical continuation methods. Springer (1990).

[2] C. Beltrán, J.-P. Dedieu, G. Malajovich, and M. Shub, Convexity properties of the condition number. SIAM. J. Matrix Anal. Appl. Volume 31, Issue 3, pp. 1491-1506 (2010).

[3] C. Beltrán, J.-P. Dedieu, G. Malajovich, and M. Shub, Convexity properties of the condition number II. Preprint (2010).

[4] C. Beltrán, and L. M. Pardo, On Smale’s 17th Problem : a Probabilistic Positive Solution. FOCM, (2008) 1-43.

[5] C. Beltrán, and L. M. Pardo, Smale’s 17th Problem : Average Polynomial Time to Compute Affine and Projective Solutions. J. AMS, 22 (2009) 363-385.

[6] C. Beltrán, and M. Shub, Complexity of Bézout’s Theorem VII : Distances Estimates in the Condition Metric, FOCM 9 (2009) 179-195.

[7] C. Beltrán, and M. Shub, On the Geometry and Topology of the Solution Variety for Polynomial System Solving (2008) https ://sites.google.com/site/beltranc/preprints

[8] L. Blum, F. Cucker, M. Shub, and S. Smale, Complexity and Real Computation, Springer, 1998.

[9] P. Boito, and J.-P. Dedieu, The condition metric in the space of rectangular full rank matrices. To appear in SIMAX.

[10] Clarke F., Optimization and Nonsmooth Analysis. J. Wiley and Sons, 1983.

[11] J.-P. Dedieu, Approximate Solutions of Numerical Problems, Condition Number Analysis and Condition Number Theorems. In : The Mathematics of Numerical Analysis, J. Renegar, M. Shub, S. Smale editors, Lectures in Applied Mathematics, Vol. 23, American Mathematical Society, 1996.

[12] J.-P. Dedieu, Points fixes, zéros et la méthode de Newton. Mathématiques et Applications, Springer, 2006.

[13] Gromov M., Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhauser, third printing 2007.

[14] T. Y. Li, Numerical solution of multivariate polynomial systems by homotopy continuation methods, Acta Numerica 6 (1997), 399-436.

[15] Overton M., An implementation of the BFGS method, http ://cs.nyu.edu/overton/software/index.html

[16] Pugh C., Lipschitz Riemann Structures. Private communication, 2007.

[17] M. Shub, Complexity of Bézout’s Theorem VI : Geodesics in the Condition Metric, FOCM 9 (2009) 171-178.

[18] M. Shub, and S. Smale, Complexity of Bézout’s Theorem I : Geometric Aspects, J. Am. Math. Soc. (1993) 6 pp.  459-501.

[19] M. Shub, and S. Smale, Complexity of Bézout’s Theorem II : Volumes and Probabilities, in : F. Eyssette, A. Galligo Eds. Computational Algebraic Geometry, Progress in Mathematics. Vol. 109, Birkhäuser, (1993).

[20] M. Shub, and S. Smale, Complexity of Bézout’s Theorem V : Polynomial Time, Theoretical Computer Science, 133, 141-164 (1994).

[21] A. Sommese, C. Wampler, The Numerical Solution of Systems of Polynomials Arising in Engineering and Science, World Scientific, 2005.

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