Solving Rank-Deficient Linear Least-Squares Problems*

Numerical solution of linear least-squares problems is a key computational task in science and engineering. Effective algorithms have been developed for the linear least-squares problems in which the underlying matrices have full rank and are well-conditioned. However, there are few efficient and robust approaches to solving the linear least-squares problems in which the underlying matrices are rank-deficient and sparse. In this paper, we propose a new method for solving rank-deficient linear least-squares problems. Our proposed method is mathematically equivalent to an existing method but has several practical advantages over the existing method. Furthermore, our proposed method is applicable to solving both dense and sparse rankdeficient linear least-squares problems. Our experimental results demonstrate the practical potential of our proposed method.