Nonlinear Equations - UFRJ
Nonlinear Equations - UFRJ
Nonlinear Equations - UFRJ
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170 BIBLIOGRAPHY<br />
[69] , Complexity of Bezout’s theorem. VI. Geodesics in the condition<br />
(number) metric, Found. Comput. Math. 9 (2009), no. 2, 171–178, DOI<br />
10.1007/s10208-007-9017-6.<br />
[70] Michael Shub and Steve Smale, Complexity of Bézout’s theorem. I. Geometric<br />
aspects, J. Amer. Math. Soc. 6 (1993), no. 2, 459–501, DOI<br />
10.2307/2152805.<br />
[71] M. Shub and S. Smale, Complexity of Bezout’s theorem. II. Volumes and<br />
probabilities, Computational algebraic geometry (Nice, 1992), Progr. Math.,<br />
vol. 109, Birkhäuser Boston, Boston, MA, 1993, pp. 267–285.<br />
[72] Michael Shub and Steve Smale, Complexity of Bezout’s theorem. III. Condition<br />
number and packing, J. Complexity 9 (1993), no. 1, 4–14, DOI<br />
10.1006/jcom.1993.1002. Festschrift for Joseph F. Traub, Part I.<br />
[73] , Complexity of Bezout’s theorem. IV. Probability of success;<br />
extensions, SIAM J. Numer. Anal. 33 (1996), no. 1, 128–148, DOI<br />
10.1137/0733008.<br />
[74] M. Shub and S. Smale, Complexity of Bezout’s theorem. V. Polynomial<br />
time, Theoret. Comput. Sci. 133 (1994), no. 1, 141–164, DOI 10.1016/0304-<br />
3975(94)90122-8. Selected papers of the Workshop on Continuous Algorithms<br />
and Complexity (Barcelona, 1993).<br />
[75] S. Smale, Topology and mechanics. I, Invent. Math. 10 (1970), 305–331.<br />
[76] Steve Smale, On the efficiency of algorithms of analysis, Bull. Amer. Math.<br />
Soc. (N.S.) 13 (1985), no. 2, 87–121, DOI 10.1090/S0273-0979-1985-15391-1.<br />
[77] , Newton’s method estimates from data at one point, computational<br />
mathematics (Laramie, Wyo., 1985), Springer, New York, 1986, pp. 185–196.<br />
[78] , Mathematical problems for the next century, Math. Intelligencer 20<br />
(1998), no. 2, 7–15, DOI 10.1007/BF03025291.<br />
[79] , Mathematical problems for the next century, Mathematics: frontiers<br />
and perspectives, Amer. Math. Soc., Providence, RI, 2000, pp. 271–294.<br />
[80] Andrew J. Sommese and Charles W. Wampler II, The numerical solution of<br />
systems of polynomials, World Scientific Publishing Co. Pte. Ltd., Hackensack,<br />
NJ, 2005. Arising in engineering and science.<br />
[81] A. M. Turing, Rounding-off errors in matrix processes, Quart. J. Mech. Appl.<br />
Math. 1 (1948), 287–308.<br />
[82] Constantin Udrişte, Convex functions and optimization methods on Riemannian<br />
manifolds, Mathematics and its Applications, vol. 297, Kluwer Academic<br />
Publishers Group, Dordrecht, 1994.<br />
[83] Jan Verschelde, Polyhedral methods in numerical algebraic geometry, Interactions<br />
of classical and numerical algebraic geometry, Contemp. Math.,<br />
vol. 496, Amer. Math. Soc., Providence, RI, 2009, pp. 243–263.<br />
[84] Wang Xinghua, Some result relevant to Smale’s reports, in: M.Hirsch, J.<br />
Marsden and S. Shub(eds): From Topolgy to Computation: Proceedings of<br />
Smalefest, Springer, new-york, 1993, pp. 456-465.