<p>An important iterative method for solving systems of linear equations or linear inequalities is the Landweber method which constructs orbits of the Landweber operator. We show that many iterative methods for solving these problems employ, actually, underrelaxations of the Landweber operator or its scaled version. We give estimations of the relaxation parameters for the operators applied in particular methods. Moreover, we present an extrapolated version of the Landweber method which is applied for solving consistent systems of linear inequalities. We show that the extrapolated Landweber method is a special case of the surrogate projection method. We also compare the numerical behavior of particular methods.</p>