Efficient Implementation of the Multishift $QR$ Algorithm for the Unitary Eigenvalue Problem
Roden Jason A. David, David S. Watkins · SIAM Journal on Matrix Analysis and Applications · 2006
We present an efficient implementation of the multishift $QR$ algorithm for computing the eigenvalues of a unitary matrix. The algorithm can perform $QR$ iterations of arbitrary degree, is conceptually simple, and is backward stable.