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Mathematics of Computation

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

Authors: Richard J. Hanson and Charles L. Lawson
Journal: Math. Comp. 23 (1969), 787-812
MSC: Primary 65.35
MathSciNet review: 0258258
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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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Keywords: Linear Least Squares, Linear Equations, Pseudoinverse Solution, Numerical Methods for Linear Equations, Orthogonal Methods for Linear Systems
Article copyright: © Copyright 1969 American Mathematical Society

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