Universality for the Toda algorithm to compute the largest eigenvalue of   a random matrix
  We prove universality for the fluctuations of the halting time for the Toda algorithm to compute the largest eigenvalue of real symmetric and complex Hermitian matrices. The proof relies on recent results on the statistics of the eigenvalues and eigenvectors of random matrices (such as delocalization, rigidity and edge universality) in a crucial way. 
Percy Deift and Thomas Trogdon
math.PR math.NA