The periodic QR algorithm is a strongly backward stable method for computing the eigenvalues of products of matrices, or equivalently for computing the eigenvalues of block cyclic matrices. The main purpose of this paper is to show that this algorithm is numerically equivalent to the standard QR algorithm. It will be demonstrated how this connection may be used to develop a better understanding of the periodic QR algorithm. (c) 2003 Elsevier Inc. All rights reserved.