QR-like algorithms for eigenvalue problems

In the year 2000 the dominant method for solving matrix eigenvalue problems is still the QR algorithm. This paper discusses the family of GR algorithms, with emphasis on the QR algorithm. Included are historical remarks, an outline of what GR algorithms are and why they work, and descriptions of the latest, highly parallelizable, versions of the QR algorithm. Now that we know how to parallelize it, the QR algorithm seems likely to retain its dominance for many years to come.