The generalized householder transformation and sparse matrices

AbstractMany algorithms for solving eigenvalue, least squares, and nonlinear programming problems require the determination of an orthogonal matrix Q such that for a given matrix C, Q transforms C into an upper triangular matrix, QC. Usually Q is a product of Householder transformations. Each transformation is a rank 1 modification of the identity matrix designed to annihilate elements in one vector. Several years ago Bronlund and Johnson proposed a generalization of the Householder transformation that is a rank k modification of the identity matrix designed to annihilate elements in k vectors simultaneously. In this paper their generalized Householder transformation is discussed in the context of sparse problems