Application of Dense Householder Transformation to a Sparse Matrix

Abstract

Householder transformations are a type of orthogonal transformation used to zero elements of a vector in many least squares and eigenvalue computations. This paper is concerned with the application of a given set of Householder transformations to a sparse matrLx X. Normally, the application of the first transformation rmns the zero structure of X. Despite this fact it is shown that the transformed matrix has some algebraic structure which might be exploited. Algorithms are given which exploit this structure during computation of the orthogonal decomposition of a matrix, the null space of a matrix, and the singular value decomposition of a matrix. © 1979, ACM. All rights reserved.