Note: I provide some preliminar versions of my published papers. The published manuscript can be found on the web site of each journal. Diego Armentano, C. Beltrán, Michael Shub ''Minimizing the discrete logarithmic energy on the sphere: The role of random polynomials''. To appear in Transactions of the American Math. Society. PDF C. Beltrán, Michael Shub. "A note on the finite variance of the averaging function for polynomial equation solving". To appear in Foundations of Computational Mathematics PDF C. Beltrán. "Estimates on the Condition Number of Random, Rank-deficient Matrices". To appear in IMA Journal of Numerical Analysis PDF C. Beltrán, Luis M. Pardo. "Smale's 17th Problem: Average Polynomial Time to compute affine C. Beltrán, Michael Shub. "Complexity of Bezout's Theorem VII: Distance Estimates in the Condition Metric" Foundations of Computational Mathematics, 9 (2009), no. 2, 179--195 DOI 10.1007/s10208-007-9018-5. PDF C. Beltrán, Luis M. Pardo. "On Smale's 17th Problem: A Probabilistic Positive answer." Foundations of Computational Mathematics. Volume 8, Number 1 (2008). PDF C. Beltrán, Luis M. Pardo. "On the Probability Distribution of Singular Varieties of Given Corank." Journal of Symbolic Computation 42 (2007), no. 1-2, 4--29. PDF C. Beltrán, Luis M. Pardo. "On the probability Distribution of Condition Numbers of Complete Intersection Varieties and the Average Radius of Convergence of Newton's Method in the Underdetermined Case."Mathematics of Computation 76 (2007), 1393-1424. PDF C. Beltrán, Luis M. Pardo. "Estimates on the Probability Distribution of Condition Number of Singular Matrices".Foundations of Computational Mathematics. Foundations of Computational Mathematics 7 (2007), no. 1, 87--134. PDF C. Beltrán, Luis M. Pardo. "On the Complexity of Non Universal Polynomial Equation Solving: Old and New Results." Foundations of Computational Mathematics: Santander 2005. L. Pardo, A. Pinkus, E. Süli, M. Todd editors (2006). Cambridge University Press. 1--35. PDF C. Beltrán. "Sobre el problema 17 de Smale: Teoría de la Intersección y Geometría Integral". Ph. D. Thesis, Universidad de Cantabria. 2006. PDF C. Beltrán, G. Dalzotto, T. Recio. "The Moment of Truth in Automatic Theorem Proving in Elementary Geometry", Proceedings of ADG 2006. PDF C. Beltrán, Luis M. Pardo. "Upper Bounds on the Distribution of the Condition Number of Singular Matrices". C. R. Math. Acad. Sci. Paris 340 (2005), no. 12, 915--919. PDF |