An inexact Krylov–Schur algorithm for the unitary eigenvalue problem

We present an efficient inexact implicitly restarted Arnoldi algorithm to find a few eigenpairs of large unitary matrices. The approximating Krylov spaces are built using short-term recurrences derived from Gragg’s isometric Arnoldi process. The implicit restarts are done by the Krylov–Schur methodology of Stewart. All of the operations of the restart are done in terms of the Schur parameters generated by the isometric Arnoldi process. Numerical results confirm the effectiveness of the algorithm.