10 citations · 23 across the 11 of their papers we have counts for
6 papers · 1 filter
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…
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.
Smale's Fundamental Theorem of Algebra reconsidered
Diego Armentano, Michael Shub
In his 1981 Fundamental Theorem of Algebra paper Steve Smale initiated the complexity theory of finding a solution of polynomial equations of one complex variable by a variant of N…
Complexity of Path-Following Methods for the Eigenvalue Problem
Diego Armentano
A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the…
Average-Case Perturbations and Smooth Condition Numbers
Diego Armentano
We define a new condition number adapted to directionally uniform perturbations. The definitions and theorems can be applied to a large class of problems. We show the relation with…