5 papers
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…
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…