This article surveys the history, development, and applications of least squares, including ordinary, constrained, weighted, and total least squares. The presentation includes proofs of the basic theory, in particular, unitary factorizations and singular-value decompositions of matrices. Numerical examples with real data demonstrate how to set up and solve several types of problems of least squares. The bibliography lists comprehensive sources for more specialized aspects of least squares.
Nievergelt, Y. (2000). Tutorial history of least squares with applications to astronomy and geodesy. Journal of Computational and Applied Mathematics, 121(1), 37–72. https://doi.org/10.1016/S0377-0427(00)00343-5