Home Publications Preprints
Note:
I provide some preliminar versions of my published papers. The
published manuscript can be found on the web site of each journal.
C.
Beltrán. "Harmonic Properties of the Logarithmic Potential and the
Computability of Elliptic Fekete Points" To appear in Constructive
Approximation (DOI: 10.1007/s00365-012-9158-y).PDF.
The final publication is available at www.springerlink.com
C. Beltrán, Luis Miguel Pardo. "Efficient Polynomial System Solving by
Numerical Methods" In Randomization, Relaxation and Complexity, Contemporary Mathematics (2011). Editors: Leonid Gurvits, Philippe P. Pébay, J. Maurice Rojas, David C. Thompson. This is an updated version of the paper with the same name mentioned below, published in the JFPTA. PDF
C. Beltrán, Anton Leykin. "Certified Numerical Homotopy Tracking". To appear in Experimental Mathematics. PDF
C. Beltrán. "A
continuation method to solve polynomial systems, and its complexity"
Numerische Mathematik 117, issue 1 (2011), 89-113 PDF
C. Beltrán, Luis Miguel Pardo. "Fast linear homotopy to find
approximate zeros of polynomial systems" Foundations of Computational
Mathematics 11, issue 1 (2011), pp 95-129 PDF
Diego Armentano, C. Beltrán, Michael Shub ''Minimizing the discrete
logarithmic energy on the sphere: The role of random polynomials''.
Transactions of the American Math. Society 363, no. 6 (2011), pp.
2955-2965 PDF
C. Beltrán. "Estimates on the Condition Number of Random,
Rank-deficient Matrices". IMA Journal of Numerical
Analysis 31, no. 1 (2011) 25--39 PDF
C. Beltrán, Jean Pierre Dedieu, Gregorio Malajovich, Michael Shub.
"Convexity properties of the condition number". SIAM Journal of Matrix
Analysis and Applications 31, no. 6 (2010), 1491-1506 PDF
C. Beltrán, Michael
Shub. "A note on the finite variance of the averaging function for
polynomial equation solving". Foundations of Computational
Mathematics 10, no. 1 (2010) 115-125 PDF
C. Beltrán, Luis Miguel Pardo. "Efficient Polynomial System Solving by
Numerical Methods" Journal of Fixed Point Theory and Applications 6,
no. 1 (2009) PDF
C. Beltrán, Luis M. Pardo. "Smale's 17th Problem: Average Polynomial Time to compute affine
and projective solutions." Journal of the American Mathematical Society, 22 (2009), 363--385 PDF
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