The authors present some results of their investigations of the design of algebraic multigrid methods. They are interested in applying these methods to solving linear systems arising from finite element discretizations of elliptic boundary value problems. They build on foundations laid by  Riemann,  Courant, Brandt, Hackbush, Bramble,  McCormick,  and many others. Optimization- and variation-oriented difference methods for material dynamics problems and material statics problems have a long history. Static linear elasticity problems are the easiest of the material statics problems, which are easier than the nonlinear material statics problems, which, in turn, are easier than the nonlinear material dynamics problems. A question of interest to me is whether these ideas can be extended to the more difficult nonlinear and dynamic problems. The authors present their fast iterative method to optimize coarse basis functions in algebraic multigrid methods (by minimizing an l₂-norm of the coarse basis functions). The first step of their minimization process gives the same result as their previous method, prolongation by smoothed aggregation. Generally, their numerical experiments suggest that adding more minimization steps improves the convergence properties; however, this is at least partially offset by the computational cost of the additional minimization steps (as usual, there is no free lunch). In summary, their computational results on static linear elasticity problems suggest that using energy-minimal basis functions improves the performance of algebraic multigrid methods.