Convergence rate of algebraic multigrid methods depends on their transfer operators being able to represent the low-energy components of the error. For many classes of problems these components are known and can easily be incorporated into the transfer operators created during the multigrid setup precedure. However, situations arise in practical applications where this knowledge is either unavailable of disguised through certain treatment of the linear system during the discretization process.

In these cases it is imperative that the algebraic solver be able to retrieve the needed information itself during its setup phase. We demonstrate that smoothed aggregation methods can provide an appropriate framework for achieving this goal. The discussion will be accompanied by preliminary computational results demonstrating that good convergence rates can be achieved even in cases where knowledge of the low-energy modes cannot be assumed.