Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 508092, 19 pages
Review Article

Least Squares for Practitioners

Department of Geomatics Engineering, Pacific Institute for the Mathematical Sciences, University of Calgary, 2500 University Drive N. W., Calgary, AB, T2N 1N4, Canada

Received 13 May 2010; Accepted 16 August 2010

Academic Editor: Alois Steindl

Copyright © 2010 J. A. Rod Blais. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In experimental science and engineering, least squares are ubiquitous in analysis and digital data processing applications. Minimizing sums of squares of some quantities can be interpreted in very different ways and confusion can arise in practice, especially concerning the optimality and reliability of the results. Interpretations of least squares in terms of norms and likelihoods need to be considered to provide guidelines for general users. Assuming minimal prerequisites, the following expository discussion is intended to elaborate on some of the mathematical characteristics of the least-squares methodology and some closely related questions in the analysis of the results, model identification, and reliability for practical applications. Examples of simple applications are included to illustrate some of the advantages, disadvantages, and limitations of least squares in practice. Concluding remarks summarize the situation and provide some indications of practical areas of current research and development.