Fast computation of eigenvalues of periodic CMV matrices

Thomas Mach; Michele Rinelli; Raf Vandebril; David Watkins

Fast computation of eigenvalues of periodic CMV matrices

Numerical Analysis 2026-07-07 v1

Authors: Thomas Mach , Michele Rinelli , Raf Vandebril , David Watkins

Abstract

Periodic CMV matrices are unitary matrices that can be specified by $O(n)$ data. Their eigenvalues can be computed by standard methods, storing them as conventional matrices (using $O(n^{2})$ data) in $O(n^{3})$ time. Here a fast method that computes the eigenvalues in $O(n^{2})$ time (using $O(n)$ data) is presented.

Keywords

CMV matrices eigenvalues fast algorithm periodic matrices unitary matrices

Cite

@article{arxiv.2607.06400,
  title  = {Fast computation of eigenvalues of periodic CMV matrices},
  author = {Thomas Mach and Michele Rinelli and Raf Vandebril and David Watkins},
  journal= {arXiv preprint arXiv:2607.06400},
  year   = {2026}
}