History
The QR algorithm was preceded by the LR algorithm, which uses the LU decomposition instead of the QR decomposition. The QR algorithm is more stable, so the LR algorithm is rarely used nowadays. However, it represents an important step in the development of the QR algorithm.
The LR algorithm was developed in the early 1950s by Heinz Rutishauer, who worked at that time as a research assistant of Eduard Stiefel at ETH Zurich. Stiefel suggested that Rutishauer use the sequence of moments y0T Ak x0, k = 0, 1, … (where x0 and y0 are arbitrary vectors) to find the eigenvalues of A. Rutishauer took an algorithm of Alexander Aitken for this task and developed it into the quotient–difference algorithm or qd algorithm. After arranging the computation in a suitable shape, he discovered that the qd algorithm is in fact the iteration Ak = LkUk (LU decomposition), Ak+1 = UkLk, applied on a tridiagonal matrix, from which the LR algorithm follows.
Read more about this topic: QR Algorithm
Famous quotes containing the word history:
“Perhaps universal history is the history of the diverse intonation of some metaphors.”
—Jorge Luis Borges (1899–1986)
“I believe my ardour for invention springs from his loins. I can’t say that the brassiere will ever take as great a place in history as the steamboat, but I did invent it.”
—Caresse Crosby (1892–1970)
“There is one great fact, characteristic of this our nineteenth century, a fact which no party dares deny. On the one hand, there have started into life industrial and scientific forces which no epoch of former human history had ever suspected. On the other hand, there exist symptoms of decay, far surpassing the horrors recorded of the latter times of the Roman empire. In our days everything seems pregnant with its contrary.”
—Karl Marx (1818–1883)