Convergence of algebraic multigrid based on smoothed aggregation. (English) Zbl 0992.65139

The authors prove an abstract convergence estimate for algebraic multigrid with a prolongation defined by disaggregation followed by a smoothing. The construction is described for the case of a general elliptic system. The condition number has polynomial growth in the number of levels.


65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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