11 citations · 29 across the 10 of their papers we have counts for
12 papers
A set of points with optimal spherical cap discrepancy
Carlos Beltrán, Jordi Marzo, Joaquim Ortega-Cerdà
We introduce an explicit deterministic collection of spherical points, $\cP_N\subset\mathbb S^2$, that we call the {\em deterministic Diamond points}. For every we prov…
Discrepancy of determinantal point processes on compact, connected two-point homogeneous spaces
Carlos Beltrán, Ujué Etayo, Giacomo Gigante +2
We study the discrepancy of point sets generated by determinantal point processes on all compact, connected two-point homogeneous spaces, namely spheres and projective…
On Gegenbauer Point Processes on the unit interval
Carlos Beltrán, Antonia M. Delgado, Lidia Fernández +1
In this note we compute the logarithmic energy of points in the unit interval chosen from different Gegenbauer Determinantal Point Processes. We check that all the differe…
How well-conditioned can the eigenvalue problem be?
Carlos Beltrán, Laurent Bétermin, Peter Grabner +1
The condition number for eigenvalue computations is a well--studied quantity. But how small can we expect it to be? Namely, which is a perfectly conditioned matrix w.r.t. eigenvalu…
On the minimum value of the condition number of polynomials
Carlos Beltrán, Fátima Lizarte
In 1993, Shub and Smale posed the problem of finding a sequence of univariate polynomials of degree with condition number bounded above by . In a previous paper by C. Beltán…
A sequence of polynomials with optimal condition number
Carlos Beltrán, Ujué Etayo, Jordi Marzo +1
We find an explicit sequence of univariate polynomials of arbitrary degree with optimal condition number. This solves a problem posed by Michael Shub and Stephen Smale in 1993.
The average condition number of most tensor rank decomposition problems is infinite
Carlos Beltrán, Paul Breiding, Nick Vannieuwenhoven
The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposi…
Approximation to uniform distribution in SO(3)
Carlos Beltrán, Damir Ferizović
Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group SO(3), with Riesz parameter up to 3. The Green functi…
The Diamond ensemble: a constructive set of points with small logarithmic energy
Carlos Beltrán, Ujué Etayo
We define a family of random sets of points, the Diamond ensemble, on the sphere depending on several parameters. Its most important property is that, for some of…
A generalization of the spherical ensemble to even-dimensional spheres
Carlos Beltrán, Ujué Etayo
In a recent article, Alishahi and Zamani discuss the spherical ensemble, a rotationally invariant determinantal point process on the 2-sphere. In this paper we extend this process…
Intrinsic potentials in locally harmonic manifolds
Carlos Beltrán, Nuria Corral, Juan G. Criado del Rey
We consider the problem of allocating a finite number of heat sources in the n-dimensional sphere. When only one such source -assumed to be of infinite temperature- is placed and a…
Average polynomial time for eigenvector computations
Diego Armentano, Carlos Beltrán, Michael Shub
We describe two algorithms for the eigenvalue, eigenvector problem which, on input a Gaussian matrix with complex entries, finish with probability 1 and in average polynomial time.