\input zb-basic \input zb-ioport \iteman{io-port 05988496} \itemau{Cui, Xiaoke; Hayami, Ken; Yin, Jun-Feng} \itemti{Greville's method for preconditioning least squares problems.} \itemso{Adv. Comput. Math. 35, No. 2-4, 243-269 (2011).} \itemab A new method to precondition general least squares problems from the perspective of the approximate Moore-Penrose inverse is presented. Similar to the robust incomplete factorization (RIF) the proposed method also includes an $A$-orthogonalization process when the coefficient matrix has full column rank. When $A$ is rank deficient, the method tries to orthogonalize the linearly independent part in $A$. A theoretical analysis on the equivalence between the preconditioned problem and the original problem is given. Based on Greville's method, a global algorithm and a vector-wise algorithm for constructing the preconditioner which is an approximate generalized inverse of $A$ is proposed. It is shown that for a full column rank matrix $A$, the developed algorithm is similar to the RIF preconditioning algorithm and includes an $A$-orthogonalization process. It is proven that under a certain assumption, using the developed preconditioner, the preconditioned problem is equivalent to the original problem, and the generalized minimal residual method (GMRES) can determine a solution to the preconditioned problem before breakdown happens. Some details on the implementation of the developed algorithms are considered, and some numerical results are presented. \itemrv{Tzvetan Semerdjiev (Sofia)} \itemcc{} \itemut{overdetermined systems; pseudoinverses; Moore-Penrose inverse; Greville algorithm; GMRES; least squares problems; robust incomplete factorization; orthogonalization; preconditioning; generalized minimal residual method; numerical results} \itemli{doi:10.1007/s10444-011-9171-x} \end