ON THE QR ALGORITHM AND UPDATING THE SVD AND THE URV DECOMPOSITION INPARALLEL

A Jacobi-type updating algorithm for the SVD or the URV decomposition is developed, which is related to the QR algorithm for the symmetric e igenvalue problem. The algorithm employs one-sided transformations, an d 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 roug hly twice as fast as the former method, while the tracking properties are preserved. The algorithm is also extended to the two-matrix QSVD o r QURV case. Finally, the differences with a number of closely related algorithms that have recently been proposed are discussed.