Complexité des méthodes homotopiques pour la résolution des systèmes polynomiaux

Jean-Pierre Dedieu[1]

  • [1] Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31069 Toulouse cedex 9, France

Les cours du CIRM (2010)

  • Volume: 1, Issue: 2, page 263-280
  • ISSN: 2108-7164

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Dedieu, Jean-Pierre. "Complexité des méthodes homotopiques pour la résolution des systèmes polynomiaux." Les cours du CIRM 1.2 (2010): 263-280. <http://eudml.org/doc/116368>.

@article{Dedieu2010,
affiliation = {Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31069 Toulouse cedex 9, France},
author = {Dedieu, Jean-Pierre},
journal = {Les cours du CIRM},
language = {fre},
number = {2},
pages = {263-280},
publisher = {CIRM},
title = {Complexité des méthodes homotopiques pour la résolution des systèmes polynomiaux},
url = {http://eudml.org/doc/116368},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Dedieu, Jean-Pierre
TI - Complexité des méthodes homotopiques pour la résolution des systèmes polynomiaux
JO - Les cours du CIRM
PY - 2010
PB - CIRM
VL - 1
IS - 2
SP - 263
EP - 280
LA - fre
UR - http://eudml.org/doc/116368
ER -

References

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  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). Zbl1203.15002
  3. C. Beltrán, J.-P. Dedieu, G. Malajovich, and M. Shub, Convexity properties of the condition number II. Preprint (2010). Zbl1203.15002
  4. C. Beltrán, and L. M. Pardo, On Smale’s 17th Problem : a Probabilistic Positive Solution. FOCM, (2008) 1-43. Zbl1153.65048MR2403529
  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. Zbl1206.90173MR2476778
  6. C. Beltrán, and M. Shub, Complexity of Bézout’s Theorem VII : Distances Estimates in the Condition Metric, FOCM 9 (2009) 179-195. Zbl1175.65058MR2496559
  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 Zbl1295.37010
  8. L. Blum, F. Cucker, M. Shub, and S. Smale, Complexity and Real Computation, Springer, 1998. Zbl0948.68068MR1479636
  9. P. Boito, and J.-P. Dedieu, The condition metric in the space of rectangular full rank matrices. To appear in SIMAX. Zbl1209.53029
  10. Clarke F., Optimization and Nonsmooth Analysis. J. Wiley and Sons, 1983. Zbl0582.49001MR709590
  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. Zbl0856.65067MR1421339
  12. J.-P. Dedieu, Points fixes, zéros et la méthode de Newton. Mathématiques et Applications, Springer, 2006. Zbl1095.65047MR2510891
  13. Gromov M., Metric Structures for Riemannian and Non-Riemannian Spaces, Birkhauser, third printing 2007. Zbl1113.53001MR2307192
  14. T. Y. Li, Numerical solution of multivariate polynomial systems by homotopy continuation methods, Acta Numerica 6 (1997), 399-436. Zbl0886.65054MR1489259
  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. Zbl1175.65060MR2496558
  18. M. Shub, and S. Smale, Complexity of Bézout’s Theorem I : Geometric Aspects, J. Am. Math. Soc. (1993) 6 pp.  459-501. Zbl0821.65035MR1175980
  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). Zbl0851.65031MR1230872
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  21. A. Sommese, C. Wampler, The Numerical Solution of Systems of Polynomials Arising in Engineering and Science, World Scientific, 2005. Zbl1091.65049MR2160078

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