A recursive procedure for computing an approximation of the left and right dominant singular subspaces of a given matrix is proposed in [1]. The method is particularly suited for matrices with many more rows than columns. The procedure consists of a few steps. In one of these steps a Householder transformation is multiplied to an upper triangular matrix. The following step consists in recomputing an upper triangular matrix from the latter product. In [1] it is said that the latter step is accomplished in O(k3) operations, where k is the order of the triangular matrix. In this short note we show that this step can be accomplished in O(k2) operations.
['Nicola Mastronardi', 'Marc Van Barel', 'Raf Vandebril']
A note on the recursive calculation of dominant singular subspaces