Least squares problems are usually written in the form

min||b－Ax ||2, A∈R

x∈R

where the norm ||・||2 stands for 2-norm. When

In this thesis, we consider constructing preconditioners for some Krylov subspace it-erative methods to solve least squares problems more efficiently. We especially focused on one kind of preconditioners, in which preconditioners are the approximate generalized inverses of the coefficient matrices of the least squares problems. We proposed two different approaches for how to construct the approximate generalized inverses of the coefficient matrices: one is based on the