Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems

The mathematical and numerical least squares solution of a general linear system of equations is discussed.Perturbation and differentiability theorems for pseudoinverses are given.Computational procedures for calculating least squares solutions using orthonormal transformations, multiplying matrices by a matrix of orthonormal basis vectors for the null-space of a given matrix, sequential processing of data, and processing of block diagonal matrices form a partial list of numerical topics presented.