T O calculate the singular value decomposition (SVD) of a real dense matrix, traditional methods start by reducing the initial matrix to a bidiagonal form, and then, calculate the SVD of the bidiagonal matrix.The process of reducing the initial matrix to bidiagonal form is known as the bidiagonalization method, which generally consists of applying successive Householder transformations from the left and right of the matrix. Since the re ‡ectors are applied on both sides of the matrix, this has a negative impact on the communication overheads of a parallel implementation for distributed memory systems.Ralha and Barlow have proposed two new methods for the reduction of dense matrices to bidiagonal form in which the Householder transformations are applied only on the right side of the matrix. This allows to de…ne all operations in terms of full columns of the matrix under transformation. Therefore, these methods are more attractive for distributed memory systems than the standard vii