Nonlinear Equations - UFRJ
Nonlinear Equations - UFRJ
Nonlinear Equations - UFRJ
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166 BIBLIOGRAPHY<br />
[12] , Smale’s 17th problem: average polynomial time to compute affine<br />
and projective solutions, J. Amer. Math. Soc. 22 (2009), no. 2, 363–385, DOI<br />
10.1090/S0894-0347-08-00630-9.<br />
[13] Carlos Beltrán and Luis Miguel Pardo, Fast linear homotopy to find approximate<br />
zeros of polynomial systems, Foundations of Computational Mathematics<br />
11 (2011), 95–129.<br />
[14] Carlos Beltrán and Michael Shub, Complexity of Bezout’s theorem. VII.<br />
Distance estimates in the condition metric, Found. Comput. Math. 9 (2009),<br />
no. 2, 179–195, DOI 10.1007/s10208-007-9018-5.<br />
[15] , On the geometry and topology of the solution variety for polynomial<br />
system solving. to appear.<br />
[16] , A note on the finite variance of the averaging function for polynomial<br />
system solving, Found. Comput. Math. 10 (2010), no. 1, 115–125, DOI<br />
10.1007/s10208-009-9054-4.<br />
[17] D. N. Bernstein, The number of roots of a system of equations, Funkcional.<br />
Anal. i Priložen. 9 (1975), no. 3, 1–4 (Russian).<br />
[18] D. N. Bernstein, A. G. Kušnirenko, and A. G. Hovanskiĭ, Newton polyhedra,<br />
Uspehi Mat. Nauk 31 (1976), no. 3(189), 201–202 (Russian).<br />
[19] Lenore Blum, Mike Shub, and Steve Smale, On a theory of computation and<br />
complexity over the real numbers: NP-completeness, recursive functions and<br />
universal machines, Bull. Amer. Math. Soc. (N.S.) 21 (1989), no. 1, 1–46,<br />
DOI 10.1090/S0273-0979-1989-15750-9.<br />
[20] Lenore Blum, Felipe Cucker, Michael Shub, and Steve Smale, Complexity<br />
and real computation, Springer-Verlag, New York, 1998. With a foreword by<br />
Richard M. Karp.<br />
[21] Paola Boito and Jean-Pierre Dedieu, The condition metric in the space of<br />
rectangular full rank matrices, SIAM J. Matrix Anal. Appl. 31 (2010), no. 5,<br />
2580–2602, DOI 10.1137/08073874X.<br />
[22] Cruz E. Borges and Luis M. Pardo, On the probability distribution of data<br />
at points in real complete intersection varieties, J. Complexity 24 (2008),<br />
no. 4, 492–523, DOI 10.1016/j.jco.2008.01.001.<br />
[23] Haïm Brezis, Analyse fonctionnelle, Collection Mathématiques Appliquées<br />
pour la Maîtrise. [Collection of Applied Mathematics for the Master’s Degree],<br />
Masson, Paris, 1983 (French). Théorie et applications. [Theory and<br />
applications].<br />
[24] W. Dale Brownawell, Bounds for the degrees in the Nullstellensatz, Ann. of<br />
Math. (2) 126 (1987), no. 3, 577–591, DOI 10.2307/1971361.<br />
[25] Peter Bürgisser and Felipe Cucker, On a problem posed by Steve Smale,<br />
Annals of Mathematics (to appear). Preprint, ArXiV, arxiv.org/abs/0909.<br />
2114v1.<br />
[26] , Conditionning. In preparation.