Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

Least Squares

  • Ali Sayfy
Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_149

Glossary

LS

Least squares

LLS

Linear least squares

MF

Model function

Definition

Least squares historically grew out of astronomy problems during the turn of the seventeenth century (Nievergelt 2000), in particular, finding trajectories of planetary motions in order to solve ocean’s navigation problems. The idea of LS was developed by Gauss, Legendre, Laplace, and many other mathematicians and scientists (Farebrother 1999). However, the first publication on LS appeared in 1805 by Legendre; he proposed the idea of minimizing the sum of squares of the errors to obtain the adjusted values of observed quantities (Plackett 1972).

Least squares” is a mathematical procedure to find the best approximate curve or surface to a given set of data points, out of different model functions that approximate the data.

Linear Least Squares

The most common application of the least squares procedure is the LS curve fitting, for which the MF forms
$$ y=f(x)={a}_1{f}_1(x)+{a}_2{f}_2(x)+\cdots...
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References

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Copyright information

© Springer Science+Business Media LLC 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsAmerican University of SharjahSharjahUAE

Section editors and affiliations

  • Suheil Khoury
    • 1
  1. 1.American University of SharjahSharjahUnited Arab Emirates