ALGEBRAIC MULTIGRID BY SMOOTHED AGGREGATION 
                FOR SECOND AND FOURTH ORDER ELLIPTIC PROBLEMS

                  Petr Vanek, Jan Mandel, and Marian Brezina

                                   Abstract

An algebraic multigrid algorithm is developed based on prolongations by
smoothed aggregation.  Coarse levels are generated automatically.  Guidelines
for the selection of method components are presented based on energy
considerations.  Efficiency of the resulting algorithm is demonstrated by
computational results.