The generalized Householder transformation and sparse matrices (Q1822453)

\textit{O. E. Brønlund} and \textit{T. L. Johnsen} [Comput. Methods Appl. Mech. Eng. 3, 153-172 (1974; Zbl 0278.65041)] have introduced a generalized Householder transformation for finding QR decompositions of a matrix. These generalizations involve rank k modifications of the identity matrix rather than the usual rank 1 modifications. In this paper the author provides an alternative method for computing the generalized Householder transformation based on Cholesky factors. The author then presents a method for finding the QR decomposition of a matrix using generalized Householder transformation. Numerical examples are presented which show that the method would not be appropriate for ill-conditioned problems, but for sparse, well-conditioned problems it requires substantially fewer arithmetic operation than the standard approach.