On the QR algorithm and updating the SVD and URV decomposition in Parallel

A Jacobi-type updating algorithm for the SVD or URV decomposition is developed, which is related to the QR algorithm for the symmetric eigenvalue problem. The algorithm employs one-sided transformations, and therefore provides a cheap alternative to earlier developed updating algorithms based on two-sided transformations. The present algorithm as well as the corresponding systolic implementation is therefore roughly twice as fast, compared to the former method, while the tracking properties are preserved. The algorithm is also extended to the 2-matrix QSVD or QURV case. Finally, the differences are discussed with a number of closely related algorithms that have recently been proposed. I. Introduction In an earlier report [14], an adaptive algorithm has been developed for tracking the singular value decomposition of a data matrix, when new observations (rows) are added continuously. The algorithm may be organized such that it provides at each time a certain approximation for the exac..