Timing comparisons of the householder QR transformations with rank-1 and rank-2 updates

The Householder QR transformation using rank-1 updates and the transformation using rank-2 updates are both O(N3) with the same cubic coefficient. While the rank-1 implementation has the smaller quadratic coefficient, the rank-2 implementation in practice is the faster algorithm, the amount of speed-up varying with the computer. This speed-up is not purely the result of replacing SAXPY operations with double GAXPY ones.