Extensions and applications of the Householder algorithm for solving linear least squares problems

Abstract

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.