RESEARCH
OUR PUBLICATIONS
| The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite
Carlos Beltrán, Paul Breiding & Nick Vannieuwenhoven | Foundations of Computational Mathematics 2021 | journal-article DOI: 10.1007/s10208-022-09551-1 Free access link |
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| On the minimum value of the condition number of polynomials
Carlos Beltrán & Fátima Lizarte | IMA Journal of Numerical Analysis 2021| journal-article DOI: 10.1093/imanum/drab070 Free access link |
| A sequence of polynomials with optimal condition number
Carlos Beltrán, Ujué Etayo, Jordi Marzo & Joaquim Ortega-Cerdà | Journal of American Mathematical Society 2020| journal-article DOI: 10.1090/jams/956 TRAILER |
| Approximation to uniform distribution in SO (3)
Carlos Beltrán & Damir Ferizović | Constructive Approximation 2020 | journal-article DOI: 10.1007/s00365-020-09506-1 TRAILER |
| The Diamond ensemble: A constructive set of spherical points with small logarithmic energy Carlos Beltrán & Ujué Etayo | Journal of Complexity 2020 | journal-article DOI: 10.1016/j.jco.2020.101471 TRAILER |
| The Real Polynomial Eigenvalue Problem is Well Conditioned on the Average Carlos Beltrán & Khazhgali Kozhasov | Foundations of Computational Mathematics 2020 | journal-article DOI: 10.1007/s10208-019-09414-2 TRAILER |
| A generalization of the spherical ensemble to even-dimensional spheres Carlos Beltrán & Ujué Etayo | Journal of Mathematical Analysis and Applications 2019 | journal-article DOI: 10.1016/j.jmaa.2019.03.004 POSTER |
| Discrete and continuous green energy on compact manifolds Carlos Beltrán, Nuria Corral & Juan G.Criado del Rey | Journal of Approximation Theory 2019 | journal-article DOI: 10.1016/j.jat.2018.09.004 TRAILER |
| Energy of the Coulomb Gas on the Sphere at Low Temperature
Carlos Beltrán & Adrien Hardy | Archive for Rational Mechanics and Analysis 2019 | journal-article DOI: 10.1007/s00205-018-1316-3 TRAILER |
| Pencil-based algorithms for tensor rank decomposition are not stable
Carlos Beltrán, Paul Breiding, and Nick Vannieuwenhoven | SIAM Journal on Matrix Analysis and Applications 2019 | journal-article DOI: 10.1137/18M1200531 TRAILER |
| The Diamond ensemble: A well distributed family of points on S2
Carlos Beltrán & Ujué Etayo | 2019 13th International Conference on Sampling Theory and Applications, SampTA 2019 2019 | conference-paper DOI: 10.1109/SampTA45681.2019.9031002 |
| The polynomial eigenvalue problem is well conditioned for random inputs
Diego Armentano & Carlos Beltrán | SIAM Journal on Matrix Analysis and Applications 2019 | journal-article DOI: 10.1137/17M1139941 |
| Asymptotically optimal designs on compact algebraic manifolds
Ujué Etayo, Jordi Marzo & Joaquim Ortega-Cerdà | Monatshefte für Mathematik 2018 | journal-article DOI: 10.1007/s00605-018-1174 |
| A stable, polynomial-time algorithm for the eigenpair problem
Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker & Michael Shub | Journal of the European Mathematical Society 2018 | journal-article DOI: 10.4171/JEMS/789 TRAILER |
| The Projective Ensemble and Distribution of Points in Odd-Dimensional Spheres
Carlos Beltrán & Ujué Etayo | Constructive Approximation 2018 | journal-article DOI: 10.1007/s00365-018-9426-6 TRAILER |
| Homotopy Continuation for Spatial Interference Alignment in Arbitrary MIMO X Networks
Carlos Beltrán, Jacobo Fanjul, Óscar González & Ignacio Santamaria | IEEE Transactions on Signal Processing 2017 | journal-article DOI: 10.1109/TSP.2016.2637310 |
| Condition Length and Complexity for the Solution of Polynomial Systems
Diego Armentano, Carlos Beltrán, Peter Bürgisser, Felipe Cucker & Michael Shub | Foundations of Computational Mathematics 2016 | journal-article DOI: 10.1007/s10208-016-9309-9 |
| Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
Carlos Beltrán, Jordi Marzo & Joaquim Ortega-Cerdà | Journal of Complexity 2016 | journal-article DOI: 10.1016/j.jco.2016.08.001 |
| On the Number of Interference Alignment Solutions for the K-User MIMO Channel With Constant Coefficients
Carlos Beltrán, Óscar González & Ignacio Santamaria | IEEE Transactions on Information Theory 2015 | journal-article DOI: 10.1109/TIT.2015.2482493 |
| A Facility Location Formulation for Stable Polynomials and Elliptic Fekete Points
Carlos Beltrán | Foundations of Computational Mathematics 2014 | journal-article DOI: 10.1007/s10208-014-9213-0 |
| A Feasibility test for linear interference alignment in MIMO channels with constant coefficients
Carlos Beltrán, Oscar Gonzalez &Ignacio Santamaría | IEEE Transactions on Information Theory 2014 | journal-article DOI: 10.1109/TIT.2014.2301440 Online Feasibility Test |
| Protein arginine methyl transferases-3 and -5 increase cell surface expression of cardiac sodium channel
Pedro Beltran-Alvarez , Alexsandra Espejo , Ralf Schmauder , Carlos Beltran & 11 more | FEBS letters 2013-07 | journal-article DOI: 10.1016/j.febslet.2013.07.043 |
| Computing the degrees of freedom for arbitrary MIMO interference channels
Carlos Beltrán, Óscar González, Christian Lameiro, Ignacio Santamaria & Javier Vía | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing – Proceedings 2013 | conference-paper DOI: 10.1109/ICASSP.2013.6638491 |
| Finding the number of feasible solutions for linear interference alignment problems
Carlos Beltrán, Óscar González & Ignacio Santamaría | IEEE International Symposium on Information Theory – Proceedings 2013 | conference-paper DOI: 10.1109/ISIT.2013.6620253 |
| Harmonic Properties of the Logarithmic Potential and the Computability of Elliptic Fekete Points
Carlos Beltrán | Constructive Approximation 2013 | journal-article DOI: 10.1007/s00365-012-9158-y |
| Robust Certified Numerical Homotopy Tracking
Carlos Beltrán & Anton Leykin | Foundations of Computational Mathematics 2013 | journal-article DOI: 10.1007/s10208-013-9143-2 |
| A general test to check the feasibility of linear interference alignment
Carlos Beltrán, Óscar González & Ignacio Santamaría | IEEE International Symposium on Information Theory – Proceedings 2012 | conference-paper DOI: 10.1109/ISIT.2012.6283962 |
| Certified numerical homotopy tracking
Carlos Beltrán &Anton Leykin | Experimental Mathematics 2012 | journal-article DOI: 10.1080/10586458.2011.606184 |
| Convexity properties of the condition number II
Carlos Beltrán, Jean-Pierre Dedieu, Gregorio Malajovich, & Mike Shub | SIAM Journal on Matrix Analysis and Applications 2012 | journal-article DOI: 10.1137/100808885 |
| On the Geometry and Topology of the Solution Variety for Polynomial System Solving
Carlos Beltrán & Michael Shub | Foundations of Computational Mathematics 2012 | journal-article DOI: 10.1007/s10208-012-9134-8 |
| A continuation method to solve polynomial systems and its complexity
Carlos Beltrán | Numerische Mathematik 2011 | journal-article DOI: 10.1007/s00211-010-0334-3 |
| Estimates on the condition number of random rank-deficient matrices
Carlos Beltrán | IMA Journal of Numerical Analysis 2011 | journal-article DOI: 10.1093/imanum/drp035 POSTER |
| Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems
Carlos Beltrán & Luis Miguel Pardo | Foundations of Computational Mathematics 2011 | journal-article DOI: 10.1007/s10208-010-9078-9 |
| Minimizing the discrete logarithmic energy on the sphere: The role of random polynomials
Diego Armentano, Carlos Beltrán & Michael Shub | Transactions of the American Mathematical Society 2011 | journal-article DOI: 10.1090/S0002-9947-2011-05243-8 |
| A note on the finite variance of the averaging function for polynomial system solving
Carlos Beltrán & Michael Shub | Foundations of Computational Mathematics 2010 | journal-article DOI: 10.1007/s10208-009-9054-4 |
| Complexity of Bezout’s Theorem VII: Distance estimates in the condition metric
Carlos Beltrán & Michael Shub | Foundations of Computational Mathematics 2009 | journal-article DOI: 10.1007/s10208-007-9018-5 |
| Convexity properties of the condition number
Carlos Beltrán, Jean-Pierre Dedieu, Gregorio Malajovich, & Mike Shub | SIAM Journal on Matrix Analysis and Applications 2009 | journal-article DOI: 10.1137/080718681 |
| Efficient polynomial system-solving by numerical methods
Carlos Beltrán & Luis Miguel Pardo | Journal of Fixed Point Theory and Applications 2009 | journal-article DOI: 10.1007/s11784-009-0113-x |
| Smale’s 17th problem: Average polynomial time to compute affine and projective solutions
Carlos Beltrán & Luis Miguel Pardo | Journal of the American Mathematical Society 2009 | journal-article DOI: 10.1090/S0894-0347-08-00630-9 |
| On smale’s 17th problem: A probabilistic positive solution
Carlos Beltran & Luis Miguel Pardo | Foundations of Computational Mathematics 2008 | journal-article DOI: 10.1007/s10208-005-0211-0 |
| Estimates on the distribution of the condition number of singular matrices
Carlos Beltran & Luis Miguel Pardo | Foundations of Computational Mathematics 2007 | journal-article DOI: 10.1007/s10208-005-0176-2 |
| 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
Carlos Beltran & Luis Miguel Pardo | Mathematics of Computation 2007 | journal-article DOI: 10.1090/S0025-5718-07-01963-1 |
| On the probability distribution of singular varieties of given corank
Carlos Beltran & Luis Miguel Pardo | Journal of Symbolic Computation 2007 | journal-article DOI: 10.1016/j.jsc.2006.05.005 |
| Upper bounds on the distribution of the condition number of singular matrices
Carlos Beltran & Luis Miguel Pardo | Comptes Rendus Mathematique 2005 | journal-article DOI: 10.1016/j.crma.2005.05.012 |
