In this paper, we study the Moore-Penrose inverse of a symmetric rank-one perturbed matrix from which a finite method is proposed for the minimum-norm least-squares solution to the system of linear equations Ax = b. This method is guaranteed to produce the required result.
The Electronic Journal of Linear Algebra
Chen, X. and Ji, J. (2011). The minimum-norm least-squares solution of a linear system and symmetric rank-one updates. Electronic Journal of Linear Algebra, 22, 480-489.