86 citations · 188 across the 17 of their papers we have counts for
9 papers · 1 filter
Pencil-based algorithms for tensor rank decomposition are not stable
Carlos Beltrán, Paul Breiding, Nick Vannieuwenhoven
We prove the existence of an open set of tensors of rank on which a popular and efficient class of algorithms for computing tensor rank decomposition…
The real polynomial eigenvalue problem is well conditioned on the average
Carlos Beltran, Khazhgali Kozhasov
We study the average condition number for polynomial eigenvalues of collections of matrices drawn from various random matrix ensembles. In particular, we prove that polynomial eige…
The polynomial eigenvalue problem is well conditioned for random inputs
Carlos Beltrán, Diego Armentano
We compute the exact value of the squared condition number for the polynomial eigenvalue problem, when the input matrices have entries coming from the standard complex Gaussian dis…
Condition length and complexity for the solution of polynomial systems
Diego Armentano, Carlos Beltrán, Peter Bürgisser +2
Smale's 17th problem asks for an algorithm which finds an approximate zero of polynomial systems in average polynomial time (see Smale 2000). The main progress on Smale's problem i…
A stable, polynomial-time algorithm for the eigenpair problem
Diego Armentano, Carlos Beltrán, Peter Bürgisser +2
We describe algorithms for computing eigenpairs (eigenvalue-eigenvector pairs) of a complex matrix . These algorithms are numerically stable, strongly accurate, and…
A stable, polynomial-time algorithm for the eigenpair problem
Peter Bürgisser, Felipe Cucker
We describe algorithms for computing eigenpairs (eigenvalue--eigenvector) of a complex matrix . These algorithms are numerically stable, strongly accurate, and theor…
The complexity and geometry of numerically solving polynomial systems
Carlos Beltran, Michael Shub
These pages contain a short overview on the state of the art of efficient numerical analysis methods that solve systems of multivariate polynomial equations. We focus on the work o…
Certified numerical homotopy tracking
Carlos Beltrán, Anton Leykin
Given a homotopy connecting two polynomial systems we provide a rigorous algorithm for tracking a regular homotopy path connecting an approximate zero of the start system to an app…
Convexity properties of the condition number
Carlos Beltrán, Jean-Pierre Dedieu, Gregorio Malajovich +1
We define in the space of n by m matrices of rank n, n less or equal than m, the condition Riemannian structure as follows: For a given matrix A the tangent space of A is equipped…