Home Page of Carlos Beltran

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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, Peter Bürgisser, Felipe Cucker, Michael Shub, "Condition Length and Complexity for the Solution of Polynomial Systems". Foundations of Computational Mathematics, volume 16, issue 6, 2016, pp 1401-1422. PDF

C. Beltrán, Jordi Marzo, Quim Ortega-Cerdŕ, "Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres". Journal of Complexity, volume 37, 2016, pp 76-109. PDF


Óscar González, C. Beltrán, Ignacio Santamaría, "On the Number of Interference Alignment Solutions for the K-User MIMO Channel with Constant Coefficients", IEEE Transaction on Information Theory, vol. 61, issue 11 (2015), pp 6028-6048. PDF

C. Beltrán, "A Facility Location Formulation for Stable Polynomials and Elliptic Fekete Points". Foundations of Computational Mathematics, volume 15, 2015, pp 125-157. PDF

C. Beltrán, Michael Shub, "The complexity and geometry of numerically solving polynomial systems". Contemporary Mathematics, volume 604, 2013, pp 71-104. PDF

Pedro Beltrán, Alexsandra Espejo, Ralf Schmauder, C. Beltrán, Ralf Morwka et al. "Protein arginine methyl transferases-3 and -5 increase cell surface expression of cardiac sodium channel". FEBS Letters 587 (2013), pp 3159-3165. PDF

Óscar González, C. Beltrán, Ignacio Santamaría, "A Feasibility Test for Linear Interference Alignment in MIMO Channels with Constant Coefficients". IEEE Transactions on Information Theory 60, no. 3 (2014), pp 1850-1856 PDF

C. Beltrán, Anton Leykin. "Robust Certified Numerical Homotopy Tracking". Foundations of Computational Mathematics. 13, no. 2 (2013), pp 253-295 PDF

C. Beltrán. "Harmonic Properties of the Logarithmic Potential and the Computability of Elliptic Fekete Points" Constructive Approximation 37 (2013), pp 135-165 PDF.
The final publication is available at www.springerlink.com

Óscar González, C. Beltrán, Ignacio Santamaría, "A general test to check the feasibility of linear interference alignment". IEEE International Symposium on Information Theory (ISIT 2012), Cambridge, MA, USA, July 2012. PDF

C. Beltrán, Michael Shub. "On the Geometry and Topology of the Solution Variety for Polynomial System Solving". Foundations of Computational Mathematics 12 (2012), pp 719-763 PDF

C. Beltrán. "The state of the art in Smale's 7th problem" in Foundations of Computational Mathematics, Budapest 2011 PDF.

C. Beltrán, Jean Pierre Dedieu, Gregorio Malajovich, Michael Shub. "Convexity properties of the condition number II". SIAM Journal of Matrix Analysis and Applications 33, no. 3 (2012), pp. 905-939 PDF

C. Beltrán, Anton Leykin. "Certified Numerical Homotopy Tracking". Experimental Mathematics 21 (1), 69-83, 2012. PDF

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. "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. IMPORTANT NOTE: there is a confusing typo in this article. In page 3 line -7 the term Gamma(n^2-2) should read Gamma(n^2-1)  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