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

Hanson, Richard J.; Lawson, Charles L.

doi:10.1090/S0025-5718-1969-0258258-9

Extensions and applications of the Householder algorithm for solving linear least squares problems
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by Richard J. Hanson and Charles L. Lawson PDF

Math. Comp. 23 (1969), 787-812 Request permission

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.

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