Centre de diffusion de revues académiques mathématiques

 
 
 
 

Les cours du CIRM

Table des matières de ce fascicule | Article précédent | Article suivant
Jean-Pierre Dedieu
Complexité des méthodes homotopiques pour la résolution des systèmes polynomiaux
Les cours du CIRM, 1 no. 2: Journées Nationales de Calcul Formel (2010), p. 263-280, doi: 10.5802/ccirm.10
Article PDF

Bibliographie

[1] E. Allgower, K. Georg, Numerical continuation methods. Springer (1990).  MR 1059455 |  Zbl 0717.65030
[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.  MR 2403529 |  Zbl 1153.65048
[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.  MR 2476778
[6] C. Beltrán, and M. Shub, Complexity of Bézout’s Theorem VII : Distances Estimates in the Condition Metric, FOCM 9 (2009) 179-195.  MR 2496559 |  Zbl 1175.65058
[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.  MR 1479636 |  Zbl 0948.68068
[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.  MR 709590 |  Zbl 0582.49001
[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.  MR 1421339 |  Zbl 0856.65067
[12] J.-P. Dedieu, Points fixes, zéros et la méthode de Newton. Mathématiques et Applications, Springer, 2006.  MR 2510891 |  Zbl 1095.65047
[13] Gromov M., Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhauser, third printing 2007.  MR 2307192 |  Zbl 1113.53001
[14] T. Y. Li, Numerical solution of multivariate polynomial systems by homotopy continuation methods, Acta Numerica 6 (1997), 399-436.  MR 1489259 |  Zbl 0886.65054
[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.  MR 2496558 |  Zbl 1175.65060
[18] M. Shub, and S. Smale, Complexity of Bézout’s Theorem I : Geometric Aspects, J. Am. Math. Soc. (1993) 6 pp.  459-501.  MR 1175980 |  Zbl 0821.65035
[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).  MR 1230872 |  Zbl 0851.65031
[20] M. Shub, and S. Smale, Complexity of Bézout’s Theorem V : Polynomial Time, Theoretical Computer Science, 133, 141-164 (1994).  MR 1294430 |  Zbl 0846.65022
[21] A. Sommese, C. Wampler, The Numerical Solution of Systems of Polynomials Arising in Engineering and Science, World Scientific, 2005.  MR 2160078 |  Zbl 1091.65049
Copyright Cellule MathDoc 2017 | Crédit | Plan du site