The least-squares problem has been widely studied and used, and only seems to become more important in this era of ever-increasing amounts of data. A good reference for numerical methods is the monograph by Björck Björck (1996). Some theoretical results can be found in Higham Higham (2002); a brief and advanced discussion can be found in Golub and Van Loan Golub & Van Loan (1996).
Note that a vast literature can also be found in statistics for what is referred to as data regression, or simply regression. Nonlinear methods for least-squares fitting of data will be discussed in the following chapter.
In modern applications one may have to deal with so-called online fitting, in which new data must continually be incorporated with old. More recent sources address related issues, e.g., in Hansen, Pereyra, and Scherer Hansen et al. (2013) and in Teunissen Teunissen (2001). The problem of geodesy and GPS positioning are discussed in some detail in Strang and Borre Strang & Borre (1997); for these applications, they describe how the updating of least squares leads to Kalman filtering.
- Björck, \AAke. (1996). Numerical Methods for Least Squares Problems. SIAM.
- Higham, N. J. (2002). Accuracy and Stability of Numerical Algorithms: Second Edition. SIAM.
- Golub, G. H., & Van Loan, C. F. (1996). Matrix Computations (3rd ed.). JHU Press.
- Hansen, P. C., Pereyra, V., & Scherer, G. (2013). Least Squares Data Fitting with Applications. JHU Press.
- Teunissen, P. J. G. (2001). Dynamic Data Processing: Recursive Least-Squares. VSSD.