3.5. Next steps#
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 [Bjorck96]. Some theoretical results can be found in Higham [Hig02]; a brief and advanced discussion can be found in Golub and Van Loan [GVL96].
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 [HPS13] and in Teunissen [Teu01]. The problem of geodesy and GPS positioning are discussed in some detail in Strang and Borre [SB97]; for these applications, they describe how the updating of least squares leads to Kalman filtering.