@Article{Joffrain:2006:AHT, author = "Thierry Joffrain and Tze Meng Low and Enrique S. Quintana-Ort\'{i} and Robert van de Geijn and Field Van Zee", title = "Accumulating {Householder} Transformations, Revisited", journal = "{ACM} Transactions on Mathematical Software", volume = "32", number = "2", pages = "169--179", month = jun, year = "2006", URL = "http://doi.acm.org/10.1145/1141885.1141886", abstract = "A theorem related to the accumulation of Householder transformations into a single orthogonal transformation, known as the compact WY transform, is presented. It provides a simple characterization of the computation of this transformation and suggests an alternative algorithm for computing it. It also suggests an alternative transformation, the UT transform, with the same utility as the compact WY Transform, which requires less computation and has similar stability properties. That alternative transformation was first published over a decade ago, but has gone unnoticed by the community.", }