Let \(W\) be a symmetric, positive definite \(m\times m\) matrix, let \(A\) be an \(m\times n\) matrix, (\(m\geq n\)) and let \(b \in \mathbb R^m\). In the rank deficient case, the generalized least squares (LS) problem \[ \min_{x\in \mathbb R^n}(Ax-b)^TW^{-1}(Ax-b) \tag{*} \] has many solutions. The authors consider an associated augumented system and obtain the minimum 2-norm solution of (*) (Section 2). In Section 3 they study the block successive overrelaxation method for the LS problem. In Section 4, they propose two preconditioned conjugate gradient (PCG) algorithms and give an error bound for the PCG method (Theorem 4.1).