Numerical Methods for Large Sparse Linear Least Squares Problems

Large sparse least squares problems arise in many applications, including geodetic network adjustments and finite element structural analysis. Although geodesists and engineers have been solving such problems for years, it is only relatively recently that numerical analysts have turned attention to them. In this paper we present a survey of numerical methods for large sparse linear least squares problems, focusing mainly on developments since the last comprehensive surveys of the subject published in 1976. We consider direct methods based on elimination and on orthogonalization, as well as various iterative methods. The ramifications of rank deficiency, constraints, and updating are also discussed.