On Row Relaxation Methods for Large Constrained Least Squares Problems

This paper addresses the question of how to construct a row relaxation method for solving large unstructured linear least squares problems, with or without linear constraints. The proposed approach combines the Herman–Lent–Hurwitz scheme for solving regularized least squares problems with the Lent–Censor–Hildreth method for solving linear constraints. However, numerical experiments show that the Herman–Lent–Hurwitz scheme has difficulty reaching a least squares solution. This difficulty is resolved by applying the Riley–Golub iterative improvement process.