Universality for the Toda algorithm to compute the largest eigenvalue of a random matrix
arXiv:1604.0738419 citationsh-index: 58
AI Analysis
Provides theoretical justification for the behavior of a numerical algorithm in random matrix settings, but is incremental as it builds on established results.
The authors prove that the halting time fluctuations of the Toda algorithm for computing the largest eigenvalue of random matrices are universal, relying on recent random matrix theory results.
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.